Question

# A survey of retirees was taken. Among other things, the retirees were asked to report the...

A survey of retirees was taken. Among other things, the retirees were asked to report the age at which they retired. Here are those 22 ages (in years). 38,42,44,47,53,54,58,59,61,62,63,67,67,68,68,69,69,72,73,74,74,76

(a) Which measures of central tendency do not exist for this data set? Choose all that apply.

Mean

Median

Mode

None of these measures

(b) Suppose that the measurement 76 (the largest measurement in the data set) were replaced by 83. Which measures of central tendency would be affected by the change? Choose all that apply.

Mean

Median

Mode

None of these measures

(c) Suppose that, starting with the original data set, the smallest measurement were removed. Which measures of central tendency would be changed from those of the original data set? Choose all that apply.

Mean

Median

Mode

None of these measures

(d) Which of the following best describes the distribution of the original data? Choose only one.

Negatively skewed

Positively skewed

Roughly symmetrical

Solution:

For the given data: 38,42,44,47,53,54,58,59,61,62,63,67,67,68,68,69,69,72,73,74,74,76

Here n=22.

a) None of these measures

Explanation: All the three measures of central tendency does exist for the given data set.

Mean= sum of all observations/ total no. Of observations

= 61.72

Mode= 67,68,69,74

b) mean

If the largest observation, 76 , were replaced by 83 then only mean would have changed as it is the only measure of Central tendency that depends on all the observations.

C) mean, median

If the smallest observation were removed then along the with the sample size, the sum of all observations would have alse changed. Hence both mean and median would have been affected.

D) negatively skewed.

As mean<median , the given data is negatively skewed.

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