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.
Application of averages
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Examples
- 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
- 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
- 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?