CHAPTER 18. STATISTICS 18.4
Relationship of the Mean, Median, and
Mode
EMBED
The relationship of themean, median, and mode to each other can provide some informationabout
the relative shape of thedata distribution. If themean, median, and mode are approximately equal
to each other, the distribution can be assumed tobe approximately symmetrical. With both the mean
and median known, thefollowing can be concluded:
- (mean - median)≈ 0 then the data is symmetrical
- (mean - median) > 0 then the data is positively skewed (skewed to the right). This means that
the median is close to the start of the data set. - (mean - median) < 0 then the data is negatively skewed (skewed to the left). This means that the
median is close to the end of the data set.
Exercise 18 - 4
- Three sets of 12 pupils each had test score recorded. The test was out of 50. Use the given data
to answer the followingquestions.
Set A Set B Set C
25 32 43
47 34 47
15 35 16
17 32 43
16 25 38
26 16 44
c 24 38 42
27 47 50
22 43 50
24 29 44
12 18 43
31 25 42Table 18.2: CumulativeFrequencies for Data Set 2.(a) For each of the sets calculate the mean and the five number summary.
(b) For each of the classes find the difference between the mean and the median. Make box
and whisker plots on thesame set of axes.
(c) State which of the three are skewed (either right or left).
(d) Is set A skewed or symmetrical?
(e) Is set C symmetrical? Why or why not?- Two data sets have the same range and interquartile range, but one isskewed right and the other
is skewed left. Sketch the box and whisker plotsand then invent data ( 6 points in each set) that
meets the requirements.
More practice video solutions or help at http://www.everythingmaths.co.za(1.) 015q (2.) 015r