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1) What is the median of the following set of scores?

a) 12

b) 13

c) 14

d) 15

2) The height of each student in a class was measured and it was found that the mean height was 160 cm. Two students were absent. When their heights were included in the data for the class, the mean height did not change.

Which of the following heights are possible for the two absent students?

a) 155 cm and 162 cm b) 152 cm and 167 cm

c) 149 cm and 171 cm d) 143 cm and 178 cm

3) This set of data is arranged in order from smallest to largest.

5, 6, 11, x, 13, 18, 25

The range is six less than twice the value of x. Which of the following is true?

a) The median is 12 and the interquartile range is 7.

b) The median is 12 and the interquartile range is 12.

c) The median is 13 and the interquartile range is 7.

d) The median is 13 and the interquartile range is 12.

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OUTLIERS

An outlier is a very high or very low score that is clearly apart from the other scores.

An outlier can occur for a variety of reasons and should always be investigated. If an outlier is found to be a value obtained through incorrect measurement or observation and is not a typical score, it can be excluded. If the outlier is a possible value from the population, it should be included in the distribution.

Outliers often have the effect of raising or lowering a mean value, but they can also affect the mode and median.

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A: 20 25 30 35 40 45

B: 20 25 30 35 40 60

C: 20 25 30 35 45 120

a) Find the mean and median of each set of scores.

b) The three data sets are the same except for the value of the last score. Investigate the effect of increasing the last score on the mean and median for set A.

c) What are the values of the mean and median of set C if the outlier 120 is not included?

ANSWERS

a)

b) Increasing the last score has no effect on the median .

As the last score increases, so the value of the mean increases. The outlier of 120 has the greatest effect on the value of the mean.

c) Set C without the score 120 has a mean and median of 30.

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