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Module 1: Measures of Central Tendency: Mean, Median, Mode

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    The mode is the value which occurs the greatest number of times in the list of data or with the greatest frequency.
    The mode is the only measure of central tendency that can be used for both quantitative and qualitative data.
    The mode is not well defined in some cases. There may also be multimodal distribution.
    If the set of data has exactly two modes, it is said to be bimodal.
    Example 1: The number of hours 8 students spent working on their science projects are as follows: 15, 11, 20, 12, 16, 15, 21, and 18. Find the mode.
    Solution: It may be convenient to list the values in ascending order:
    11
    12
    15
    15
    16
    18
    20
    21
    The number that appears with the greatest frequency is 15. Therefore, the mode is 15 hours.
    Example 2: The number of seedlings that germinated in each flat of 20 flats containing 32 seeds each are listed in the following chart:
    27
    28
    31
    29
    27
    24
    32
    19
    23
    22
    22
    27
    29
    30
    28
    21
    28
    25
    24
    30
    Find the mode, if one exists.
    Solution: Arrange the numbers in ascending order:
    19
    21
    22
    22
    23
    24
    24
    25
    27
    27
    27
    28
    28
    28
    29
    29
    30
    30
    31
    32
    The number 27 appears with a frequency of 3.The number 28 appears with a frequency of 3.Therefore, the set of numbers is bimodal, with modes of 27 and 28.
    Example 3: The number of wins in a game of chess for each of 5 students are listed below:
    John
    5
    Mary
    10
    William
    8
    James
    4
    Tanya
    7
    Find the mode.
    Solution: The mode is the student with the most wins.The student with the most wins is Mary. Therefore, the mode is 10.