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Get Full Access to Elementary Statistics - 12 Edition - Chapter 3.4 - Problem 5cre
Get Full Access to Elementary Statistics - 12 Edition - Chapter 3.4 - Problem 5cre

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Descriptive Statistics Use the hand lengths in Exercise

ISBN: 9780321836960 18

Solution for problem 5CRE Chapter 3.4

Elementary Statistics | 12th Edition

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Problem 5CRE

Descriptive Statistics Use the hand lengths in Exercise 1 and find the following: (a) mean; (b) median; (c) standard deviation; (d) variance; (e) range. Include the appropriate units of measurement.

Step-by-Step Solution:
Step 1 of 3

Solution 5CRE

(a)

We know that the mean of a given set of observations obtained by adding those observations and divide that result with number of given observations. The mean hand length ( in millimeters) of the given sample is

Therefore, the mean of the given data set is 190.125 millimeters.

(b)

We know that median is the positional average, first arrange the given observations in an order either ascending or descending order. If the given observations are odd in number then pick the middle observation in the sorted list, which represents the median of the given data set. If they are even in number, then pick middle two observations in the sorted list and find its average, which gives the median of the given data set. The sorted list of given observations in ascending order are and they are even in number. The middle observations are 195 and196, mean of these two is the median of the given set of observations.

Therefore, the median of the given data set is 195.5 millimeters.

(c)

From the given information, . We know that standard deviation of the given data set found as follows:

Therefore, the standard deviation  of the given data set is 18.673 millimeters.

(d)

We know that, square of the standard deviation is the variance.

Therefore, the variance of the given data set is.

(e)

From the given information, maximum data value is 214 millimeters and minimum data value is 158 millimeters in the given data set. We know that range of the given set of sample values found as follows:

Therefore, the range of the given set of observations is 56 millimeters.

Step 2 of 3

Step 3 of 3

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