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Questions and Answers
Questions and Answers
In the context of descriptive analytics, what inherent limitation exists when relying solely on frequency distributions for summarizing large, complex datasets?
In the context of descriptive analytics, what inherent limitation exists when relying solely on frequency distributions for summarizing large, complex datasets?
- The reduction of data into discrete categories within frequency distributions inevitably introduces information loss, precluding nuanced understanding of underlying patterns and anomalies. (correct)
- The computational complexity associated with constructing frequency distributions for datasets exceeding terabytes in scale exceeds the capabilities of current processing architectures.
- Frequency distributions are inherently biased toward categorical data, obscuring insights from continuous numerical variables and their interdependencies.
- Frequency distributions are incapable of capturing the temporal dynamics and longitudinal trends present within datasets that evolve over extended time intervals.
Considering a dataset comprising a bimodal distribution with significant skewness, which measure of central tendency would most accurately reflect the 'typical' value, and what caveat must be considered?
Considering a dataset comprising a bimodal distribution with significant skewness, which measure of central tendency would most accurately reflect the 'typical' value, and what caveat must be considered?
- The median, understanding that it is robust to outliers and skewness but may not capture the full complexity of the bimodal nature of the distribution. (correct)
- The mode, recognizing its sensitivity to minor fluctuations within the dataset and potential instability across different subsamples.
- The arithmetic mean, acknowledging that it might be significantly influenced by the extreme values within the skewed portion of the distribution.
- A trimmed mean, computed after excluding a predetermined percentage of extreme values from both tails of the distribution to reduce the impact of the skewness.
How does the application of the COUNTIFS function differ from the COUNTIF function in a sophisticated, multi-criteria assessment of data integrity within a financial transaction dataset?
How does the application of the COUNTIFS function differ from the COUNTIF function in a sophisticated, multi-criteria assessment of data integrity within a financial transaction dataset?
- COUNTIF is capable of handling criteria that incorporate complex regular expressions, providing a mechanism for detecting subtle anomalies indicative of fraudulent activities within transaction records.
- COUNTIFS provides an integrated capability for handling missing data values, accommodating incomplete transaction records without introducing bias into the resulting frequency counts.
- While COUNTIF can only assess a single criterion, it possesses superior computational efficiency when operating on extremely large datasets containing millions of transaction entries.
- COUNTIFS allows for the simultaneous evaluation of multiple, logically independent criteria across different data ranges, facilitating identification of transactions meeting stringent compliance standards. (correct)
When tasked with identifying differentially expressed genes from RNA-seq data across multiple experimental conditions, what specific considerations dictate the choice between using simple frequency counts versus more sophisticated statistical models?
When tasked with identifying differentially expressed genes from RNA-seq data across multiple experimental conditions, what specific considerations dictate the choice between using simple frequency counts versus more sophisticated statistical models?
In the context of descriptive analytics, how does the strategic deployment of 'pivot tables' in a high-dimensional dataset address the inherent challenges associated with information overload and pattern recognition?
In the context of descriptive analytics, how does the strategic deployment of 'pivot tables' in a high-dimensional dataset address the inherent challenges associated with information overload and pattern recognition?
What is the core challenge in using graphical representations of frequency distributions, such as histograms, to effectively communicate insights derived from a highly skewed dataset containing numerous outliers?
What is the core challenge in using graphical representations of frequency distributions, such as histograms, to effectively communicate insights derived from a highly skewed dataset containing numerous outliers?
In scenarios where decisions must be made about resource allocation based on measures of central tendency, what critical assessment should be performed before choosing between the arithmetic mean and the weighted mean, particularly when analyzing customer lifetime value?
In scenarios where decisions must be made about resource allocation based on measures of central tendency, what critical assessment should be performed before choosing between the arithmetic mean and the weighted mean, particularly when analyzing customer lifetime value?
Why is the median considered a more robust measure of central tendency than the mean when analyzing income distributions in a population characterized by significant wealth inequality?
Why is the median considered a more robust measure of central tendency than the mean when analyzing income distributions in a population characterized by significant wealth inequality?
Considering customer purchase behavior data for a subscription-based service, what inferential challenges arise when using the mode to determine the most 'popular' subscription plan, and how can these be mitigated?
Considering customer purchase behavior data for a subscription-based service, what inferential challenges arise when using the mode to determine the most 'popular' subscription plan, and how can these be mitigated?
What statistical caveat should be meticulously addressed when interpreting percentile ranks, and is this especially vital when comparing student performance across different cohorts within a longitudinal educational study?
What statistical caveat should be meticulously addressed when interpreting percentile ranks, and is this especially vital when comparing student performance across different cohorts within a longitudinal educational study?
When applying measures of position, such as quartiles, in inventory management, what potential pitfalls arise from relying solely on historical sales data from previous years without accounting for external factors?
When applying measures of position, such as quartiles, in inventory management, what potential pitfalls arise from relying solely on historical sales data from previous years without accounting for external factors?
What inherent mathematical assumption underlies the interpretation of the interquartile range (IQR) as a robust measure of data spread, and how does this assumption impact its applicability in real-world datasets?
What inherent mathematical assumption underlies the interpretation of the interquartile range (IQR) as a robust measure of data spread, and how does this assumption impact its applicability in real-world datasets?
When interpreting the coefficient of variation (CV), what critical consideration must be taken into account regarding the nature and scale of the underlying data, particularly when comparing variability across disparate datasets?
When interpreting the coefficient of variation (CV), what critical consideration must be taken into account regarding the nature and scale of the underlying data, particularly when comparing variability across disparate datasets?
How does the strategic selection of data visualization techniques mitigate the risk of conveying spurious correlations when presenting descriptive analytics findings to stakeholders with varying degrees of statistical acumen?
How does the strategic selection of data visualization techniques mitigate the risk of conveying spurious correlations when presenting descriptive analytics findings to stakeholders with varying degrees of statistical acumen?
What inherent limitation exists when using bar charts to represent categorical data with a large number of categories, and how can this limitation be effectively addressed to maintain interpretability?
What inherent limitation exists when using bar charts to represent categorical data with a large number of categories, and how can this limitation be effectively addressed to maintain interpretability?
How do you characterize a perfect correlation with both Pearson and Spearman correlation coefficients?
How do you characterize a perfect correlation with both Pearson and Spearman correlation coefficients?
In what way should be considered that Spearman correlation will be useful to descriptive analysis?.
In what way should be considered that Spearman correlation will be useful to descriptive analysis?.
If during correlation analysis you only can compute Pearson, which considerations should be taken in account?
If during correlation analysis you only can compute Pearson, which considerations should be taken in account?
How could be defined the difference between Pearson and Spearman when applying descriptive data analysis to a data set?
How could be defined the difference between Pearson and Spearman when applying descriptive data analysis to a data set?
Why the interpretation of coefficient of the Pearson correlation can vary, and how those coefficients can mis interpreted?
Why the interpretation of coefficient of the Pearson correlation can vary, and how those coefficients can mis interpreted?
Is there an association in which could be represented in the Point-Biserial correlation?.
Is there an association in which could be represented in the Point-Biserial correlation?.
Simple linear regression analysis models have two essential characteristics, these are:.
Simple linear regression analysis models have two essential characteristics, these are:.
What the advantage about multiple linear regression models?
What the advantage about multiple linear regression models?
Let's compare the usage between correlation and regression, how is the most accurate description between them?
Let's compare the usage between correlation and regression, how is the most accurate description between them?
What does a positive slope in regression analysis mean from a math perspective?.
What does a positive slope in regression analysis mean from a math perspective?.
If the P-value of a correlation is smaller than the statistical significance value, how should be considered said hypothesis test?
If the P-value of a correlation is smaller than the statistical significance value, how should be considered said hypothesis test?
When is not appropriate to apply linear regression models:
When is not appropriate to apply linear regression models:
When performing diagnostic analytics in website visitor data, imagine a scenario where the sales team implements an A/B test. A hypothesis is that the sales team might be impacting the website. How this should be approached?
When performing diagnostic analytics in website visitor data, imagine a scenario where the sales team implements an A/B test. A hypothesis is that the sales team might be impacting the website. How this should be approached?
What does diagnostic analytics involves in terms of root cause explanation?
What does diagnostic analytics involves in terms of root cause explanation?
In diagnostic insights, how Inferential Statistics provide value about the construction of the hypotesis?
In diagnostic insights, how Inferential Statistics provide value about the construction of the hypotesis?
If you were analyzing a potential relationship between different data points, which tool does not belong in inferential statistics?
If you were analyzing a potential relationship between different data points, which tool does not belong in inferential statistics?
In a test scenario, which factor could produce unreliable inferential statistics?
In a test scenario, which factor could produce unreliable inferential statistics?
What problem can arise when using a bar chart?.
What problem can arise when using a bar chart?.
When outliers are presents, what is the best measure of central tendecy, mean or median?.
When outliers are presents, what is the best measure of central tendecy, mean or median?.
When you have different groups, what is helpful about percentiles rank
When you have different groups, what is helpful about percentiles rank
Why using external metrics with external components helps, in order to mitigate the effect of overreliance in old and historical data?.
Why using external metrics with external components helps, in order to mitigate the effect of overreliance in old and historical data?.
If external market trends are not that useful for your analysis, and you still needed to assess them, how can make them useful:.
If external market trends are not that useful for your analysis, and you still needed to assess them, how can make them useful:.
Questions and Answers
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Flashcards
Flashcards
Summary Statistics
Summary Statistics
Numerical values that describe and summarize key characteristics of a dataset.
Measures of Frequency
Measures of Frequency
Measures how often a particular value/category appears in a dataset, summarizing data distributions.
Count (frequency, f)
Count (frequency, f)
Number of times a particular value/category occurs in a dataset.
Relative Frequency (Percentage, %)
Relative Frequency (Percentage, %)
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Cumulative Frequency
Cumulative Frequency
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Cumulative Relative Frequency
Cumulative Relative Frequency
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Frequency Distribution
Frequency Distribution
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Categorical Data Frequency Distribution
Categorical Data Frequency Distribution
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Ungrouped Frequency Distributions
Ungrouped Frequency Distributions
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Grouped Frequency Distributions
Grouped Frequency Distributions
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Bar Graph
Bar Graph
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Histogram
Histogram
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Pie Chart
Pie Chart
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Frequency Polygon
Frequency Polygon
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COUNT (Excel Function)
COUNT (Excel Function)
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COUNTIF (Excel function)
COUNTIF (Excel function)
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COUNTIFS (Excel function)
COUNTIFS (Excel function)
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Pivot Table
Pivot Table
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FREQUENCY function
FREQUENCY function
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Measure of Central Tendency
Measure of Central Tendency
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Arithmetic Mean
Arithmetic Mean
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Weighted Mean
Weighted Mean
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Median
Median
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Mode
Mode
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Measures of Position
Measures of Position
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Quartile
Quartile
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Decile
Decile
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Percentile
Percentile
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Measures of Variability and Dispersion
Measures of Variability and Dispersion
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Range
Range
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Interquartile Range (IQR)
Interquartile Range (IQR)
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Quartile Deviation(QD)
Quartile Deviation(QD)
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Standard Deviation
Standard Deviation
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Variance
Variance
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Coefficient of Variation (CV)
Coefficient of Variation (CV)
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Data Visualization
Data Visualization
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Bar Charts
Bar Charts
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Pie Charts
Pie Charts
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Histogram
Histogram
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Line Chart
Line Chart
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Study Notes
Study Notes
Descriptive Analytics
- Descriptive analytics is about summarizing and understanding the key features of a dataset through numerical values.
- It helps in understanding the distribution, central tendency, variability, and patterns within data.
- This makes analyzing and interpreting large datasets easier.
Summary Statistics Categories
- Summary statistics can be categorized into measures of frequency, central tendency, position, variability, and shape of distribution.
Measures of Frequency
- Measures how often a particular value or category appears in a dataset.
- Summarizes and interprets data distributions.
Count (Frequency, f)
- This refers to the number of times a particular value or category occurs in a dataset.
Relative Frequency (Percentage, %)
- This refers to the proportion or percentage of occurrences of a specific value compared to the total number of values in a dataset.
- For example, if a class survey finds that 8 students prefer coffee out of 40 total students, the relative frequency is 20%.
Cumulative Frequency
- The cumulative frequency refers to the sum of frequencies for all values up to a certain point in the dataset, which helps in understanding the distribution pattern.
Cumulative Relative Frequency
- The cumulative relative frequency refers to the cumulative frequency expressed as a percentage of the total number of observations.
- For example, if a class survey finds that 8 students prefer coffee out of 40 total students (a relative frequency of 20%) and 12 students prefer tea (a relative frequency of 30%), the cumulative frequency for coffee and tea is 20 students, with a cumulative relative frequency of 50%.
Frequency Distribution
- This is a systematic way of organizing data to show how often each value or range of values occurs.
- It can be a table or graphical representation that organizes data into different categories or intervals.
- It helps summarize large datasets, making it easier to identify patterns, trends, and distributions within the data.
Categorical Data
- Categorical data is Qualitative (non-numerical) data, such as gender, favorite color, or mode of transportation.
Ungrouped Frequency Distributions
- Used when the dataset is small or consists of distinct values.
- Data is presented as individual values along with their frequencies.
Grouped Frequency Distributions
- Used when the dataset is large and covers a wide range of values.
- Data is grouped into class intervals with their corresponding frequencies.
Graphical Representations of Frequency Distributions
- Bar graphs summarize categorical data, displaying data using rectangles of the same width for each category, usually with gaps between the bars, and they can be oriented horizontally or vertically.
- Histograms summarize numerical data measured on an interval scale, and are commonly used in exploratory data analysis to illustrate data distribution features.
- Pie Charts display data in a circular graph, where the entire pie represents 100% of a whole, and the slices represent portions of the whole.
- Frequency polygons are line graphs that represent frequency distributions, created by plotting class frequencies against class midpoints and connecting the points with straight lines.
Measures of Frequency using EXCEL
- COUNT is used to count the number of cells that contain numbers.
- COUNTIF is used to count cells based on one criteria.
- COUNTIFS is used to count cells based on multiple criteria
- To use countif, use the syntax "=COUNTIF (range, criteria)"
- range - The range of cells to count.
- criteria - The criteria that controls whichcells should be counted.
COUNTIFS Function
- The syntax "=COUNTIFS (range1, criteria1, [range2], [criteria2], ..)" is used.
PIVOT Table
- Steps to insert a pivot table:
- Click any single cell inside the data set.
- On the Insert tab, in the Tables group, click PivotTable.
- Excel will display the Pivot Table window to be filled in.
- The PivotTable Fields pane appears.
- To build a pivot table, drag fields into one the Columns, Rows, or Values area.
FREQUENCY Function
- The FREQUENCY function returns a frequency distribution, which is a list that shows the frequency of values at given intervals.
- The syntax is "=FREQUENCY (data_array, bins_array)".
- data_array is an array of values for which you want to get frequencies.
- bins_array is an array of intervals ("bins") for grouping values.
- To create a frequency distribution using FREQUENCY:
- Enter numbers that represent the bins you want to group values into.
- Make a selection the same size as the range that contains bins, or one greater if want to include the extra item.
- Enter the FREQUENCY function as a multi-cell array formula with control+shift+enter.
- The syntax is "=FREQUENCY (data_array, bins_array)".
Measures of Central Tendency
- Describes a set of data by identifying the central position in the data set as a single value.
- It is important, because it is used in business analytics, helps in educational research and is common in IT applications.
Arithmetic Mean
- The most common type of average, calculated by summing all values and dividing by the number of values.
Weighted Mean
- A calculation that assigns varying degrees of importance to the numbers in a particular data set
- It is a statistical method that calculates the average by multiplying the weights with their respective mean and taking its sum.
Why Consider the Arithmetic Mean? Why Consider the Weighted Mean?
- Arithmetic Mean:
- Is a simple average of values.
- Is used with all values contribute equally to the final result.
- Is easy to compute and interpret.
- Weighted Mean:
- Is an average that accounts for different weights (importance).
- It is used when some values have more impact based on frequency, importance, or relevance.
- It is a more accurate representation when data points have different significance.
Key Takeaways for Data Analysts:
- Use Arithmetic Mean when summarizing data with equal contribution from each value.
- Use Weighted Mean when some values carry more importance in decision-making.
- Real-world analytics often require Weighted Mean to reflect actual trends and business impact.
Median (centermost/middlemost)
- The median is the middle value in an ordered dataset.
- For an odd number of values, it is the exact middle value.
- For an even number of values, the median is the average of the two middle values.
- Unlike the mean, the median is not affected by extreme values, making it useful for skewed data.
- Better Representation in Skewed Distributions: In cases where a few extremely high or low values distort the mean, the median gives a more realistic central value.
Mode
- The most frequently occurring observation in a data set. (value that has the highest frequency)
- A data distribution with one mode value is called unimodal whereas distributions with more than one mode values is called multimodal (they can be bimodal, trimodal etc.)
- The mode is useful when dealing with non-numeric data (e.g., most popular product, most common user preference).
- Handles Skewed Data Well: Unlike the mean, which is affected by extreme values, the mode simply identifies the most frequent occurrence.
- It helps in identifying customer trends, popular products, and high-demand categories.
Measures of Position
- Measures of position refer to statistical measures that describe the relative position of a data value within a dataset.
QUARTILE
- Divides the distribution into four equal parts
- Q1 (25th percentile): Lower quartile, first 25% of data.
- Q2 (50th percentile / Median): Middle value of the dataset.
- Q3 (75th percentile): Upper quartile, top 25% of data.
DECILE
- Divides the distribution ten equal parts. For example, the 2nd decile represents the value below which 20% of the data falls.
PERCENTILE
- Divides the distribution into one hundred parts.
- For instance, the 90th percentile indicates the value below which 90% of the data falls.
Applications of Measures of Position
- Student Performance Classification:
- Teachers can divide students' scores into four groups (Q1, Q2, Q3, Q4).
- Q1 (Lowest 25%): Students needing remedial classes
- Q2 (25% - 50%): Average-performing students
- Q3 (50% - 75%): Above-average students
- Teachers can divide students' scores into four groups (Q1, Q2, Q3, Q4).
- Scholarship and Admission Criteria:
- Schools may set eligibility criteria based on quartiles (e.g., only students in the top 25% qualify for scholarships).
- Schools may admit students based on top percentiles (e.g., top 10% of senior high school graduates).
- Growth and Progress Monitoring:
- Schools use percentile ranks to track student growth over time.
- Example: A student moving from the 40th percentile to the 60th percentile shows improvement.
- Schools use percentile ranks to track student growth over time.
- Sales Performance Analysis:
- Identifying top and low-performing sales representatives
- Percentiles: If a salesperson's monthly revenue is in the 90th percentile, they are among the top 10% of performers.
- Quartiles: Sales reps below the 25th percentile (Q1) may require training or incentives to improve.
- Identifying top and low-performing sales representatives
- Customer Segmentation & Targeting:
- Quartiles: Customers in the top Q3 (75th percentile and above) are high-value customers and can receive loyalty rewards.
- Inventory Management & Stock Levels:
- Quartiles: Items in the bottom 25% of sales (Q1) might be phased out, while those in Q3 and Q4 need restocking.
- Percentiles: Products below the 20th percentile (P20) are slow-moving and may need promotional strategies.
Measures of Variability and Dispersion
- Measures of Variability and Dispersion describe how spread out or scattered a dataset is.
- It is a method of measuring the degree by which numerical data or values tend to spread from cluster about central point of average.
- Includes Range, Interquartile Range, Quartile Deviation, Standard Deviation, Variance and Coefficient of Variation.
Range
- The Range is the difference between the lowest and highest values.
- Range = Highest(max) – Lowest(min)
Interquartile Range
- Measures the spread of the middle 50% of the data, reducing the impact of outliers.
- IQR =Q3 - Q1
Quartile Deviation
- The Quartile Deviation(QD) is the product of half of the difference between the upper(Q3) and lower quartiles (Q1).
- Quartile Deviation = (Q3- Q1) / 2
Standard Deviation
- The Standard Deviation is a measure of how spread out numbers are, how concentrated the data are around the mean.
- The standard deviation is zero if all the observations are constant
- The standard deviation measures how concentrated the data are around the mean; the more concentrated, the smaller the standard deviation.
- A small standard deviation means that the values in a statistical data set are close to the mean of the data set, on average, and a large standard deviation means that the values in the data set are farther away from the mean, on average.
- The standard deviation can never be a negative number, due to the way it's calculated and the fact that it measures a distance (distances are never negative numbers).
Variance
- Variance is a numerical value that describes the variability of observations from its arithmetic mean.
Example Applications of Standard Deviation
- Researchers examining student test scores can use the standard deviation to determine whether most students perform at or close to the average or whether test scores are all over the place.
- Real estate agents calculate the standard deviation of house prices in a particular area so they can inform their clients of the type of variation in house prices they can expect.
- A weatherman who works in a city with a small standard deviation in temperatures year-round can confidently predict what the weather will be on a given day.
Coefficient of Variation
- The coefficient of variation (CV) of a data set is defined as:
- CV = S / M
- S is the standard deviation of the data set and M is its mean (average).
- CV = S / M
- The coefficient of variation can give us an idea of how the standard deviation compares to the mean:
- A CV of less than 1 means that the standard deviation is low and is less than the mean.
- A CV of more than 1 means that the standard deviation is high and is greater than the mean.
Data Visualization
- Data visualization is the graphical representation of information and data.
- It helps communicate data clearly and effectively using visual elements like charts, graphs, and maps.
- It makes data easier to understand, identifies trends, supports decision-making and enhances storytelling with data.
- Insights are communicated through visualizations following data collection, cleansing, and analysis.
- It is used to find patterns and outliers in exploratory data analysis (EDA).
Visualizations for Categorical Data
- Bar chart
- Summarizes categorical data, displaying data using rectangles of the same width for each category, usually with gaps between the bars, and they can be oriented horizontally or vertically.
- Pie Chart
- Displays data in a circular graph, where the entire pie represents 100% of a whole, and the slices represent portions of the whole.
Visualizations for Numerical Data
- Histogram
- Summarizes numerical data measured on an interval scale, and are commonly used in exploratory data analysis to illustrate data distribution features.
- Box Plot (Box-and-Whisker Plot)
- Provides a five-number summary (minimum, first quartile, median, third quartile and maximum), a compact view of data's central tendency, spread, and variability.
Visualizations for Time-Series Data
- Line Chart
- Commonly used to display change over time as a series of data points connected by straight line segments on two axes.
Visualizations for Relationships
- Scatter plot
- Used to display the relationship between two variables, consisting of points plotted on a Cartesian coordinate system, where each point represents a pair of values-one for the independent variable (on the x-axis) and one for the dependent variable (on the y-axis).
Inferential Statistics
- Inferential statistics is a branch of statistics that allows us to make predictions or generalizations about a larger population based on a sample of data, and goes beyond the immediate dataset to estimate parameters, test hypotheses, and predict future trends.
- Common methods include:
- Estimation: Predicts population parameters using sample data.
- Hypothesis Testing: Tests assumptions about a population.
- Correlation Analysis: Measures the strength and direction of relationships between variables
- Regression Analysis: Examines relationships between variables.
Diagnostic Analytics
- Diagnostic analytics focuses on understanding why something happened by identifying the root causes of trends, patterns, or anomalies in data.
Key Features of Diagnostic Analytics:
- Root Cause Analysis: Identifies patterns, anomalies, or correlations that explain outcomes.
- Data Drilling: Involves "drilling down" into data layers to uncover insights.
- Statistical Methods: Uses techniques such as correlation analysis and regression analysis.
Examples of Diagnostic Analytics:
- Sales Decline: Sales in one region fell due to a supply chain delay.
- Website Traffic: A social media campaign boosted traffic.
- Student Performance results: Students who missed review sessions scored lower.
The Role of Inferential Statistics in Diagnostic Analytics:
- Hypothesis Testing in Diagnostics: Inferential statistics provides hypothesis testing methods that help validate relationships between variables in diagnostic analytics.
- Correlation Analysis: Diagnostic analytics often relies on inferential techniques like correlation analysis to determine whether variables are associated.
- Regression Analysis: Inferential statistics uses regression models to predict relationships, which diagnostic analytics can use to identify root causes of trends.
Correlation
- Correlation is a measure of relationship between two or more variables used to test relationships between quantitative or categorical variables where the degree of the relationship between variables is expressed in into perfect correlation, some degree of correlation and no correlation.
Types of correlation:
- A positive correlation is a relationship between two variables in which both variables move in the same direction.
- A negative correlation is a relationship between two variables where an increase in one variable is associated with a decrease in the other.
- A zero correlation exists when there is no relationship between two variables.
- It's important to know that correlation is not causation".
Correlation coefficient
-
The correlation coefficient is a statistical measure of the strength of a linear relationship between two variables where
- Perfect correlation is either positive or negative (+1 and -1)
- Correlation coefficients may be positive or negative (+.01 to +.99 and -.01 to -.99)
- A zero correlation is represented by 0 where coefficients are defined as.
- 0.00 – 0.199 Very Weak
- 0.20 – 0.399 Weak
- 0.40 – 0.599 Medium
- 0.60 – 0.799 Strong
- 0.80 – 1.000 Very Strong
-
Spearman correlation:
- This type of correlation is used to determine the monotonic relationship or association between two datasets.
- Unlike the Pearson correlation coefficient, it's based on the ranked values for each dataset and uses skewed or ordinal variables rather than normally distributed ones.
Pearson correlation:
- The Pearson and Spearman correlation coefficients can range in value from −1 to +1 where, For the Pearson correlation coefficient to be +1, when one variable increases then the other variable increases by a consistent amount. This relationship forms a perfect line where The Spearman correlation coefficient is also +1 in this case where the opposite is also true, and coefficients can be +-.
Point-Biserial Correlation
- A correlation measure of the degree of relationship between two variables where one variable is continuous(ratio or interval) and the other is dichotomous (binary)nominal variable using sample questions including:
- Is there an association between gender (female, male) with the income earned?
- Is there an association between age group (elderly, not elderly) and satisfaction with life?
Regression Analysis
- Regression analysis is a statistical method used to estimate the relationships between two or more variables:
- Independent variables (explanatory variables, or predictors) are the factors that might influence the dependent variable.
- Dependent variable (criterion variable/response variable/controlled variable) is the main factor you are trying to understand and predict.
- Regression Types:
- Simple linear regression models the relationship between a dependent variable and one independent variables using a linear function.
Examples may include expenses in gas based on the distance traveled and monthly sales based on advertising costs
- Simple linear regression means there is only one independent variable X which changes result on different values for Y with the model formula y = a + bx where: x is the value of the independent variable y is the value of the dependent variable a is a constant, the y-intercept, which shows the value of y when the value of x=0. On a regression graph, it's the point where the line crosses the y axis b - the regression coefficient, is the slope of a regression line, which shows the rate of change for y as x changes
- Simple linear regression models the relationship between a dependent variable and one independent variables using a linear function.
Examples may include expenses in gas based on the distance traveled and monthly sales based on advertising costs
a positive (direct) relationship and, if there are an independent slope means that two variables are positively related with examples including plant growth to amount of fertilizer provided.
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