Sampling, Data & Statistics

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Questions and Answers

In probability sampling, which technique ensures every member has an equal chance of being selected?

  • Convenience sampling
  • Simple random sampling (correct)
  • Stratified sampling
  • Snowball sampling

Which of the following is not a standard type of data presentation?

  • Tabular form
  • Textual form
  • Graphical form
  • Predictive form (correct)

What is the best description of data presentation?

  • The process of collecting primary data
  • The process of analyzing numerical data
  • The process of testing hypotheses
  • The process of comparing data using visual aids (correct)

What constitutes a population in research?

<p>The entire group being studied (D)</p> Signup and view all the answers

What is the main purpose of using a frequency distribution table?

<p>To summarize data in rows and columns (A)</p> Signup and view all the answers

The mode of a dataset is:

<p>The most frequently occurring value (D)</p> Signup and view all the answers

Which of the following is an example of ordinal data?

<p>Customer satisfaction ratings (e.g. Satisfied, Neutral) (D)</p> Signup and view all the answers

What is the purpose of data encoding?

<p>To convert raw data into a structured format for analysis (A)</p> Signup and view all the answers

In statistics, what does Q1 (First Quartile) represent?

<p>The 25th percentile (A)</p> Signup and view all the answers

What is an advantage of graphical presentation over textual presentation?

<p>It is easier to interpret trends and patterns (A)</p> Signup and view all the answers

Which of the following is not a measure of central tendency?

<p>Standard deviation (D)</p> Signup and view all the answers

In systematic sampling, how are samples selected?

<p>Every nth item is chosen after a random start (B)</p> Signup and view all the answers

What is a pie chart best used for?

<p>Displaying proportions of a whole (C)</p> Signup and view all the answers

What is the highest level of measurement that has a true zero point?

<p>Ratio (A)</p> Signup and view all the answers

Why is stratified sampling used in research?

<p>To ensure that subgroups are represented (D)</p> Signup and view all the answers

Which of the following represents secondary data?

<p>A company's financial report from last year (C)</p> Signup and view all the answers

What is the difference between mean and median?

<p>The mean is the sum of all values divided by the number of values, while the median is the middle value (C)</p> Signup and view all the answers

How does tabular presentation differ from graphical presentation?

<p>Tabular uses numbers in rows and columns, while graphical uses charts and graphs (C)</p> Signup and view all the answers

What distinguishes qualitative data from quantitative data?

<p>It consists of descriptive or categorical data (D)</p> Signup and view all the answers

What is the primary function of data analysis?

<p>To make sense of data and identify trends (A)</p> Signup and view all the answers

In the data set 5, 9, 12, 15, 18, what is the median?

<p>12 (C)</p> Signup and view all the answers

If a student's exam scores are 75, 80, 85, 90, and 95, what is the percentile rank of 85?

<p>60th percentile (D)</p> Signup and view all the answers

Given the data set: 12, 18, 24, 30, 36, 42, 48, what is the mean?

<p>30 (A)</p> Signup and view all the answers

A researcher wants to conduct a survey among high school students in a city. He divides the students by grade level (Grade 7, Grade 8, Grade 9, Grade 10) and selects a proportionate number from each grade. What sampling technique is used?

<p>Stratified Sampling (D)</p> Signup and view all the answers

What does the first quartile (Q1) of a dataset represent?

<p>The value below which 25% of the observations lie (A)</p> Signup and view all the answers

Find the mode of the following data set: 3, 7, 7, 12, 15, 15, 15, 20, 22

<p>15 (C)</p> Signup and view all the answers

A frequency distribution table shows that 10 students scored between 80-90 marks in a test. What does this indicate?

<p>10 students scored within the range of 80 to 90 (B)</p> Signup and view all the answers

You are given the following dataset: 10, 20, 30, 40, 50. If the standard deviation is approximately 14.1, what does this tell you about the data?

<p>The data is widely spread out (D)</p> Signup and view all the answers

If you want to visually represent the relationship between two numerical variables, which type of graph should you use?

<p>Scatter plot (D)</p> Signup and view all the answers

A business analyst uses a line graph to show how sales have changed over five years. What insight does this graphical form provide?

<p>Trends in sales performance over time (A)</p> Signup and view all the answers

A teacher collected quiz scores from 100 students and wanted to divide them into percentiles to see the distribution of performance. What should she do?

<p>Divide the students into four equal groups (C)</p> Signup and view all the answers

A health researcher is analyzing data on patient recovery times. The mean recovery time is 10 days, but the median is 8 days. What does this suggest?

<p>There are outliers pulling the mean higher (D)</p> Signup and view all the answers

You are given two datasets: Dataset A: {15, 20, 25, 30, 35} Dataset B: {10, 10, 10, 10, 50} Which dataset has a higher standard deviation?

<p>Dataset B (D)</p> Signup and view all the answers

A company conducts a survey on customer satisfaction. If 90% of respondents gave ratings between 4 and 5 (on a scale of 1 to 5), what measure of central tendency would best describe this dataset?

<p>Mode (D)</p> Signup and view all the answers

If a histogram shows a right-skewed distribution, what does this mean about the data?

<p>The majority of values are concentrated on the lower end (D)</p> Signup and view all the answers

Why is systematic sampling sometimes preferred over simple random sampling?

<p>It is easier to implement and follows a fixed pattern (D)</p> Signup and view all the answers

A study finds that as the number of study hours increases, exam scores also increase. What kind of relationship does this indicate?

<p>Positive correlation (C)</p> Signup and view all the answers

A researcher is investigating the relationship between income level and spending habits. Which data collection method would provide the most reliable insights?

<p>Conducting structured surveys with a large sample (B)</p> Signup and view all the answers

What is the interquartile range (IQR) useful for?

<p>Measuring the spread of the middle 50% of data (C)</p> Signup and view all the answers

Which of the following would be an appropriate conclusion if a dataset’s mean is much higher than its median?

<p>The dataset is positively skewed (A)</p> Signup and view all the answers

A researcher decided to use cluster sampling instead of simple random sampling. What is the main reason for this?

<p>Cluster sampling is more cost-effective (D)</p> Signup and view all the answers

What does a scatter plot showing a downward trend suggest?

<p>A negative correlation (B)</p> Signup and view all the answers

Why might a pie chart not be the best choice for presenting annual sales trends over five years?

<p>It does not effectively represent changes over time (C)</p> Signup and view all the answers

A survey was conducted among employees to determine their job satisfaction on a Likert scale (1-5). What type of data is this?

<p>Ordinal (B)</p> Signup and view all the answers

A company collected data on customer spending habits and found extreme values (outliers) in the dataset. Which measure of central tendency is least affected by these outliers?

<p>Median (A)</p> Signup and view all the answers

A data analyst is choosing between a bar graph and a histogram to represent data. When should a histogram be used instead of a bar graph?

<p>When data is continuous and grouped into intervals (B)</p> Signup and view all the answers

If a scatter plot shows randomly scattered points with no clear pattern, what does this suggest about the relationship between the two variables?

<p>No correlation (A)</p> Signup and view all the answers

A school principal wants to compare students' test scores before and after implementing a new teaching strategy. Which data presentation method would best show improvement over time?

<p>Line graph (B)</p> Signup and view all the answers

In a study on student study habits, researchers surveyed only students from one school. What is a potential issue with this research method?

<p>The results may not be generalizable to other schools (A)</p> Signup and view all the answers

Why is it important to pilot test a questionnaire before conducting a full-scale survey?

<p>To test if the questionnaire is clear and effective (A)</p> Signup and view all the answers

Flashcards

Simple random sampling

Ensures each member has an equal chance of being selected, eliminating bias.

Data presentation

Organizing and displaying data to make it understandable using visual aids.

Population (in research)

The entire group of individuals, objects, or events that are the subject of a study.

Frequency distribution table

Organizes data by grouping values and displaying their frequencies.

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Mode

The most frequently occurring value in a dataset.

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Ordinal data

Categories with a meaningful order but no fixed intervals.

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Data encoding

Convert raw data into a structured format for analysis.

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Q1 (First Quartile)

The value below which 25% of the data falls.

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Advantage of graphical presentation

Easier to interpret trends and patterns compared to textual presentation.

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Standard deviation

Measures data spread, not central tendency.

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Systematic sampling

Every nth item is chosen after a random start.

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Pie chart best use

Displaying proportions of a whole.

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Ratio data

The highest level of measurement that has a true zero point.

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Why use stratified sampling

To ensure that subgroups are represented.

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Secondary data

Previously collected information.

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Mean vs. Median

The sum of all values divided by the number of values, while the median is the middle value.

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Tabular vs. Graphical presentation

Tabular uses numbers in rows and columns, while graphical uses charts and graphs.

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Qualitative data

Consists of descriptive or categorical data.

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Primary function of data analysis

To make sense of data and identify trends.

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Median of 5, 9, 12, 15, 18

The middle value of the dataset is 12.

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Percentile rank of 85

85 is higher than 60% of the data points.

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Mean of 12, 18, 24, 30, 36, 42, 48

Mean = (12+18+24+30+36+42+48) / 7 = 30.

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Stratified Sampling

The researcher ensures representation from each grade.

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First quartile (Q1)

The value below which 25% of the observations lie

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Mode of: 3, 7, 7, 12, 15, 15, 15, 20, 22

The most frequently occurring value is 15

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Frequency distribution table

10 students scored within the range of 80 to 90.

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Large standard deviation.

The data is widely spread out

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Visual relationship?

Scatter plots show relationships between two numerical variables.

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See change?

Line graphs show trends and changes over time.

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Students and groups

Divide the students into hundred equal groups.

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Is mean shifted?

There are outliers pulling the mean higher

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Dataset variability

Dataset B has more variability.

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Which measure best represents?

The most frequent value represents customer ratings best.

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Does the mean match the median?

The majority of values are concentrated on the lower end.

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Benefit of fixed sampling

It is easier to implement and follows a fixed pattern

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Scores Increase by hours?

Causal relationship

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Measuring spread in middle!

Measuring the spread of the middle 50% of data

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Comparing Mean and median trend

The dataset will be positively skewed when the mean is much higher.

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Reason to use cheaper sampling

Cluster sampling is more cost-effective.

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When is there an overall decrease?

A negative correlation

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Study Notes

  • Simple random sampling gives each population member an equal selection chance.
  • Predictive form is not a standard type of data presentation.
  • Data presentation organizes data with visuals to aid understanding and comparison.
  • A research population is the entire group under study.
  • Frequency distribution tables group data to show patterns and trends.
  • The mode is the most frequent value in a dataset.
  • Ordinal data has ordered categories with no fixed intervals, such as satisfaction ratings.
  • Data encoding converts raw data to a structured format for analysis.
  • Q1 (First Quartile) represents the 25th percentile.
  • Graphical presentation makes it easier to see trends and patterns compared to textual presentation.
  • Standard deviation is a measure of data spread, not central tendency.
  • Systematic sampling selects every nth item after a random start.
  • Pie charts best display proportions of a whole.
  • Ratio data has a true zero point.
  • Stratified sampling ensures representation from subgroups.
  • Secondary data comes from previously collected information, such as financial reports.
  • The mean is the average; the median is the middle value.
  • Tabular presents numbers in rows/columns; graphical uses charts/graphs.
  • Qualitative data is descriptive/categorical, while quantitative data is numerical.
  • Data analysis makes sense of data and identifies trends.
  • In the data set 5, 9, 12, 15, 18, the median is 12.
  • A student's exam score of 85 is at the 60th percentile given scores of 75, 80, 85, 90, and 95.
  • Given the data set: 12, 18, 24, 30, 36, 42, 48, the mean is 30.
  • Stratified sampling is used when a proportional number from each grade are analyzed.
  • The first quartile (Q1) is the value below which 25% of the observations lie.
  • The mode of the data set: 3, 7, 7, 12, 15, 15, 15, 20, 22 is 15.
  • A frequency distribution table indicates 10 students scored within the range of 80 to 90.
  • A standard deviation of approximately 14.1 indicates that the data is widely spread out.
  • To visually represent the relationship between two numerical variables, use a Scatter plot.
  • A line graph of sales over five years shows trends in sales performance over time.
  • Teachers divide students into 100 equal parts to determine percentiles.
  • A mean recovery time of 10 days and a median of 8 days suggests outliers pull the mean higher.
  • Dataset B: {10, 10, 10, 10, 50} has a higher standard deviation.
  • The mode best describes if 90% of respondents gave ratings between 4 and 5.
  • A right-skewed distribution has values concentrated on the lower end.
  • Systematic sampling follows a fixed pattern.
  • An increase in study hours and exam scores indicates a positive correlation.
  • Structured surveys with a large sample provide the most reliable insights.
  • Interquartile range (IQR) is useful for measuring the spread of the middle 50% of data.
  • A dataset is positively skewed if the mean is much higher than its median.
  • Cluster sampling is more cost-effective than simple random sampling.
  • A downward trend on a scatter plot suggests a negative correlation.
  • Pie charts do not represent changes over time effectively.
  • Customer satisfaction on a Likert scale (1-5) is what type of data? - Ordinal data
  • The median is the measure of central tendency least affected by outliers.
  • Histograms should be used instead of bar graphs with continuous data that is grouped into intervals.
  • Randomly scattered points on a scatter plot show no correlation.
  • A line graph best shows improvement over time.
  • Limiting student study habits information to one school is a lack of generalizability.
  • To verify if a questionnaire is clear and effective pilot testing is useful.

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