Finding Mode of Grouped Data
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Questions and Answers

What is the total number of observations in the given data?

  • 51 (correct)
  • 40
  • 46
  • 195

    • What is the value of 'l' in the formula for calculating the median?

  • 150
  • 145 (correct)
  • 140
  • 155

    • What is the percentage of girls who are taller than the median height?

  • 75%
  • 60%
  • 50% (correct)
  • 40%

    • What is the formula for calculating the median from a frequency distribution table?

    <p>Median = l + (n / 2 - cf) / f</p> Signup and view all the answers

    What is the median height of the girls in the given data?

    <p>149.03 cm</p> Signup and view all the answers

    What is the characteristic of a data set with more than one value having the same maximum frequency?

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

    What is the purpose of the frequency distribution table in finding the mode of ungrouped data?

    <p>To visualize the frequency of each data value</p> Signup and view all the answers

    In a grouped frequency distribution, what is the term for the class with the maximum frequency?

    <p>Modal class</p> Signup and view all the answers

    What is the formula to calculate the mode in a grouped frequency distribution?

    <p>Mode = l + ((f1 - f0) / (2f1 - f0 - f2)) × h</p> Signup and view all the answers

    What is the assumption made while using the formula to calculate the mode in a grouped frequency distribution?

    <p>All class sizes are equal</p> Signup and view all the answers

    What is the significance of the lower limit of the modal class (l) in the formula for calculating the mode?

    <p>It represents the starting point of the modal class</p> Signup and view all the answers

    What is the value of the median marks when n = 26.5, l = 60, cf = 22, f = 7, and h = 10?

    <p>66.4</p> Signup and view all the answers

    In the survey of the heights of 51 girls, what is the number of girls with height in the interval 140 - 145?

    <p>7</p> Signup and view all the answers

    What is the type of distribution given in the survey of the heights of 51 girls?

    <p>Less than type</p> Signup and view all the answers

    What is the frequency of the class interval below 140?

    <p>4</p> Signup and view all the answers

    What is the total number of girls in the survey?

    <p>51</p> Signup and view all the answers

    What is the formula used to calculate the median in the given problems?

    <p>Median = l + (h / f) * (n - cf)</p> Signup and view all the answers

    What is the purpose of converting the data into continuous classes in question 4?

    <p>To find the median of the data</p> Signup and view all the answers

    What is the total number of policy holders in the data given in question 3?

    <p>100</p> Signup and view all the answers

    What is the range of the class interval in which the median of the distribution in question 2 lies?

    <p>20 - 30</p> Signup and view all the answers

    What is the number of consumers in the class interval 125 - 145 in the frequency distribution in question 1?

    <p>20</p> Signup and view all the answers

    What is the condition for a person to be eligible for a policy in the data given in question 3?

    <p>Age should be between 18 years and 60 years</p> Signup and view all the answers

    What is the number of leaves in the class interval 145 - 153 in the data given in question 4?

    <p>12</p> Signup and view all the answers

    What is the formula to find the mode for grouped data?

    <p>Mode = l + ((f1 - f0) / (2 * f1 - f0 - f2)) * h</p> Signup and view all the answers

    What is the purpose of ensuring that the class intervals are continuous when calculating mode and median for grouped data?

    <p>To ensure the formulae can be applied correctly</p> Signup and view all the answers

    What is the cumulative frequency of a class?

    <p>The frequency obtained by adding the frequencies of all the classes preceding the given class</p> Signup and view all the answers

    What is the purpose of the NOTE TO THE READER in the passage?

    <p>To emphasize the importance of continuous class intervals</p> Signup and view all the answers

    What is the formula for the median of grouped data?

    <p>Median = l + ((n / 2) - cf) / f * h</p> Signup and view all the answers

    Study Notes

    Median for Grouped Data

    • The median for grouped data is calculated using the formula: Median = l + (n/2 - cf) × h / f
    • n is the total frequency, l is the lower limit of the median class, cf is the cumulative frequency of the class preceding the median class, h is the class size, and f is the frequency of the median class

    Example 1: Calculating Median

    • Given the values: n = 26.5, l = 60, cf = 22, f = 7, and h = 10
    • The median is calculated as: Median = 60 + (26.5 - 22) × 10 / 7 = 66.4

    Example 2: Finding Median Height

    • A survey of 51 girls' heights (in cm) is conducted, and the data is obtained: Less than 140: 4, Less than 145: 11, Less than 150: 29, Less than 155: 40, Less than 160: 46, and Less than 165: 51
    • The class intervals are: Below 140, 140-145, 145-150, 150-155, 155-160, and 160-165
    • The frequency distribution table is constructed, and the median height is calculated using the formula: Median = 145 + (25.5 - 11) × 5 / 18 = 149.03

    Mode for Grouped Data

    • The mode for grouped data is calculated using the formula: Mode = l + (f1 - f0) × h / (2f1 - f0 - f2)
    • l is the lower limit of the modal class, h is the size of the class interval, f1 is the frequency of the modal class, f0 is the frequency of the class preceding the modal class, and f2 is the frequency of the class succeeding the modal class

    Example 3: Finding Mode

    • The wickets taken by a bowler in 10 cricket matches are: 2, 6, 4, 5, 0, 2, 1, 3, 2, 3
    • The frequency distribution table is constructed, and the mode is found to be 2

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    Description

    Learn how to calculate the mode of grouped data, including identifying multimodal data and understanding the concept of a single mode. This quiz covers the basics of mode calculation and its applications.

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