A manager at UPS collected a sample of five boxes with the f

A manager at UPS collected a sample of five boxes with the following weights: 48, 24, 28, 12, and 40.

(a) Compute the range.

(b) Compute the variance.

(c) Compute the standard deviation.

Solution

A) arrange the data in accending order

12,24,28,40,48

range will be (12,48)

B) First, I added up all of the numbers:
12 + 24 + 28 + 40 + 48 = 152

I squared the total, and then divided the number of items in the data set
152 x 152 = 23104
23104 / 5 = 4620.8

I took my set of original numbers from step 1, squared them individually this time, and added them all up:
(12 x 12) + (24 x 24) + (28 x 28) + (40 x 40) + (48 x 48) = 5408

I subtracted the amount in step 2 from the amount in step 3:
5408 - 4620.8 = 787.1999999999998

I subtracted 1 from the number of items in my data set:
5 - 1 = 4

I divided the number in step 4 by the number in step 5:
787.1999999999998 / 4 = 196.79999999999995
This is my Variance!

C) Finally, I took the square root of the number from step 6 (called the Variance),
(196.79999999999995) = 14.028542333400145
This is my Standard Deviation!