Question

a survey of 8 retirees was taken. among other things, the retirees were asked to report the age at which they retired. here are those 8 ages (in years): 71, 61, 67, 63, 62, 55, 66, 61. (a) what is the median of this data - set? if your answer is not an integer, round your answer to one decimal place. (b) what is the mean of this data - set? if your answer is not an integer, round your answer to one decimal place. (c) how many modes does the data - set have, and what are their values? indicate the number of modes by clicking in the appropriate circle, and then indicate the value(s) of the mode(s), if applicable. zero modes one mode: two modes: and

Explanation:

Step1: Arrange data in ascending order

55, 61, 61, 62, 63, 66, 67, 71

Step2: Calculate the median

Since there are \(n = 8\) data - points (an even number of data - points), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th ordered values. \(\frac{n}{2}=4\) and \(\frac{n}{2}+1 = 5\). The 4th value is 62 and the 5th value is 63. Median\(=\frac{62 + 63}{2}=62.5\approx62.5\)

Step3: Calculate the mean

Mean\(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}=\frac{55+61+61+62+63+66+67+71}{8}=\frac{506}{8}=63.25\approx63.3\)

Step4: Find the mode

The mode is the value that appears most frequently in the data - set. The number 61 appears twice, and all other numbers appear only once. So, there is one mode, which is 61.

Answer:

(a) 62.5
(b) 63.3
(c) one mode
(d) 61