Consider the data set below:
Note:
a) Find the five-number summary (Show work.)
b) Compute the sample mean and the sample standard deviation (include symbols with answers.)
So, the sample mean is
Step 1 :Given the data set:
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
Step 4 :The first quartile (Q1) is
Step 5 :The median (Q2) is
Step 6 :The third quartile (Q3) is
Step 7 :The maximum value is
Step 8 :So, the five-number summary is
Step 9 :The sample mean is the sum of all the values divided by the number of values. The sample mean is
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
Step 11 :So, the sample mean is