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Statistics and Data Analysis
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Statistics and Data Analysis

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Questions and Answers

What percentage of data items are below the first quartile (Q1)?

  • 100%
  • 25% (correct)
  • 75%
  • 50%

    • How do you compute the second quartile (Q2)?

  • By finding the mean of the entire data set
  • By finding the median of the lower half of the data
  • By finding the median of the entire data set (correct)
  • By finding the median of the upper half of the data

    • What is the purpose of finding the inter-quartile range?

  • To identify outliers in the data (correct)
  • To find the mean of the data
  • To find the median of the data
  • To find the mode of the data

    • How do you find the third quartile (Q3)?

    <p>By finding the median of the upper half of the data</p> Signup and view all the answers

    What is the median of the lower half of the data called?

    <p>First quartile (Q1)</p> Signup and view all the answers

    What is the purpose of ordering the data set in ascending order?

    <p>To prepare the data for quartile computation</p> Signup and view all the answers

    What is the second quartile (Q2) also known as?

    <p>Median</p> Signup and view all the answers

    What percentage of data items are above the third quartile (Q3)?

    <p>25%</p> Signup and view all the answers

    What is the main approach to handling missing values in numeric fields?

    <p>Using the mean value</p> Signup and view all the answers

    What is the default value for Field1 in the given scenario?

    <p>0</p> Signup and view all the answers

    What is the mode of the categorical field in the given scenario?

    <p>A</p> Signup and view all the answers

    How do you handle missing values in categorical fields when there is no mode?

    <p>Use a default value</p> Signup and view all the answers

    What is an outlier in a dataset?

    <p>A data value that deviates from expected values</p> Signup and view all the answers

    What is the purpose of handling missing values in a dataset?

    <p>To ensure the accuracy and completeness of the data</p> Signup and view all the answers

    What is the interquartile range related to in the context of outliers?

    <p>The limits of the data range</p> Signup and view all the answers

    Why is it necessary to handle outliers in a dataset?

    <p>To prevent them from affecting the analysis</p> Signup and view all the answers

    What is the formula to calculate the Interquartile Range (IQR)?

    <p>IQR = Q3 - Q1</p> Signup and view all the answers

    What is the purpose of calculating the Interquartile Range (IQR)?

    <p>To identify outliers in the data</p> Signup and view all the answers

    How do you determine if a data point is an outlier using the Interquartile Range (IQR)?

    <p>If the value is greater than Q3 + 1.5*IQR</p> Signup and view all the answers

    What is the purpose of smoothing noisy data?

    <p>To correct errors in the data</p> Signup and view all the answers

    What is the first step in handling noisy data?

    <p>Validation and correction</p> Signup and view all the answers

    What is the middle value of the data when it is ordered in ascending order?

    <p>Median</p> Signup and view all the answers

    What is the purpose of calculating the quartiles (Q1, Q2, and Q3)?

    <p>To understand the distribution of the data</p> Signup and view all the answers

    How do you calculate the first quartile (Q1) of a data set?

    <p>Q1 = median of the lower half of the data</p> Signup and view all the answers

    What is the result of the calculation Q3 - Q1?

    <p>Interquartile Range (IQR)</p> Signup and view all the answers

    What is the purpose of using the Interquartile Range (IQR) to detect outliers?

    <p>To identify data points that are significantly different from the majority of the data</p> Signup and view all the answers

    Study Notes

    Handling Missing Values

    • A set of fields with missing values can be handled using default values, mean values, or random values.
    • There is no mode in the given list of numbers: 13, 15, 12, 17, 22, 11, 19.
    • When handling missing values using means and modes, the mean is used for numeric fields and the mode is used for categorical fields.
    • If the mode doesn't exist, a default value or a random value can be used.
    • For numeric fields, the mean is calculated and approximated if necessary.
    • For categorical fields, the mode is calculated from the existing values.

    Handling Missing Values (Using Means and Modes)

    • Field1 mean = 17.44
    • Field3 mean = 334.44
    • Field4 mean = 81.78
    • Field2 is categorical, and its mode is A.

    Handling Missing Values (Using Random Values)

    • No additional information provided.

    Handling Outliers

    • Outliers are data values that deviate from expected values of the rest of the data set.
    • Outliers are extreme values that lie near the limits of the data range or go against the trend of the remaining data.
    • Outliers need more investigation to make sure they don't contain errors.

    Handling Outliers Using Inter-quartile Range

    • The inter-quartile range (IQR) is used to detect outliers.
    • Q1, Q2, and Q3 are calculated using the following steps:
      • Order the data set in ascending order.
      • Use the median to divide the ordered data set into two halves.
      • The median is the second quartile (Q2).
      • The first quartile (Q1) is the median of the lower half of the data.
      • The third quartile (Q3) is the median of the upper half of the data.

    Computing Q1, Q2, and Q3

    • Example #1: Q1 = 15, Q2 = 40, Q3 = 43
    • Example #2: Q1 = 17, Q2 = 37.5, Q3 = 40

    Detecting Outliers using Inter-quartile Range

    • IQR is calculated as Q3 - Q1.
    • A data value is an outlier if it is less than (Q1 - 1.5IQR) or greater than (Q3 + 1.5IQR).
    • Example: Data set 75000, -40000, 10000000, 50000, 99999 does not contain outliers.
    • Example: Data set 75000, 40000, 10000000, 50000, 99999, 75000 contains an outlier, 10000000.

    Noisy Data

    • Noisy data are data that have incorrect values.
    • Reasons for noisy data include:
      • Faulty data collection instruments
      • Human or computer errors during data entry
      • Transmission errors
      • Technology limitations

    Smoothing Noisy Data

    • Smoothing noisy data corrects errors using:
      • Validation and correction
      • Standardization

    Validation and Correction of Noisy Data

    • This step examines the data for data-entry errors and tries to correct them automatically as far as possible using:
      • Spell checking based on dictionary lookup for identifying and correcting misspellings.

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    Quiz Team

    Description

    This quiz covers concepts related to statistical analysis, including data occurrence and handling missing values.

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