Problem

Consider the data set below:
263337444647505255636772
Note: x2=31,266
a) Find the five-number summary (Show work.)
b) Compute the sample mean and the sample standard deviation (include symbols with answers.)

Answer

Expert–verified
Hide Steps
Answer

So, the sample mean is 49.33 and the sample standard deviation is 13.69

Steps

Step 1 :Given the data set: 26,33,37,44,46,47,50,52,55,63,67,72

Step 2 :The five-number summary of a data set consists of the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum. These values can be calculated using the sorted data set.

Step 3 :The minimum value is 26

Step 4 :The first quartile (Q1) is 42.25

Step 5 :The median (Q2) is 48.5

Step 6 :The third quartile (Q3) is 57.0

Step 7 :The maximum value is 72

Step 8 :So, the five-number summary is 26,42.25,48.5,57.0,72

Step 9 :The sample mean is the sum of all the values divided by the number of values. The sample mean is 49.33

Step 10 :The sample standard deviation is the square root of the variance, which is the average of the squared differences from the mean. The variance is 187.33 and the standard deviation is 13.69

Step 11 :So, the sample mean is 49.33 and the sample standard deviation is 13.69

link_gpt