Application of averages

Application of averages

Similar to previous sections about median and mode, and mean, in this section we practice calculating the median, mode, and mean of given data sets in word problems. The mean, median, and mode are measures of central tendency. A measure of central tendency is a value that represents the centre of a set of data. Also, in this section, we are given data sets in word problems and asked to figure out which measure of central tendency best describes the data. The mode is the best measure of central tendency for data that represents frequency of choice. In contrast, the median is the best measure if a data set contains unusually large or small numbers in relation to the rest of the data. Finally, either the median or mean can be used as a measure of central tendency if all of the numbers in a set of data are close together.

Lessons

  • 1.
    A school collected gifts from students to give to needy children in the community over the Christmas holidays. The following numbers of gifts were collected.

    Grade

    Total number of gifts collected

    1

    65

    2

    100

    3

    70

    4

    54

    5

    45

    6

    54

    7

    43

    a)
    What are the median and mean? Round your answer to the nearest whole number.

    b)
    Which value is an outlier?

    c)
    If the outlier is removed, what is the new mean? Round your answer to the nearest whole number.

    d)
    Which measure of central tendency better describes the data? Explain why.


  • 2.
    The following table represents the sizes of winter boots that were sold last week.

    Size

    5

    6

    7

    8

    9

    10

    Number Sold

    3

    2

    4

    4

    0

    1

    a)
    What are the mean and mode sizes of shoes sold? Round your mean to the nearest whole shoe size.

    b)
    If you were in charge of ordering in more boots, which measure of central tendency is more meaningful? Why?


  • 3.
    In a running race, the mean time was 2 minutes; the mode time was 2 minutes and 10 seconds; and the median time was 1 minute and 55 seconds. Jack had a time of 2 minutes. Which measure of central tendency (mode, median or mean) would you use to make Jack feel like he could do better?