The time (in minutes) that it takes 20 people to complete a task follows. 30 35...
The time (in minutes) that it takes 20 people to complete a task follows. 30 35 51 65 22 35 44 55 30 50 40 60 64 38 52 68 38 53 62 49 a. Find the interquartile range. b. Find the mean of the data. c. Find the standard deviation of the data. d. Find the coefficient of variation.
Homework Answers
( a ) Interquartile range :
The interquartile range is the difference between the third and first quartiles.
The third quartile is 57.5.
The first quartile is 36.5.
The interquartile range = 57.5 - 36.5 = 21.
The interquartile range of the data set is 21.
( b ) Mean :
Mean = sum of terms / number of terms
= 941/ 20
= 47.05
Mean = 47.05
( c ) standard deviation :
Create the following table.
| data | data-mean | (data - mean)2 |
| 30 | -17.05 | 290.7025 |
| 35 | -12.05 | 145.2025 |
| 51 | 3.95 | 15.6025 |
| 65 | 17.95 | 322.2025 |
| 22 | -25.05 | 627.5025 |
| 35 | -12.05 | 145.2025 |
| 44 | -3.05 | 9.3025 |
| 55 | 7.95 | 63.2025 |
| 30 | -17.05 | 290.7025 |
| 50 | 2.95 | 8.7025 |
| 40 | -7.05 | 49.7025 |
| 60 | 12.95 | 167.7025 |
| 64 | 16.95 | 287.3025 |
| 38 | -9.05 | 81.9025 |
| 52 | 4.95 | 24.5025 |
| 68 | 20.95 | 438.9025 |
| 38 | -9.05 | 81.9025 |
| 53 | 5.95 | 35.4025 |
| 62 | 14.95 | 223.5025 |
| 49 | 1.95 | 3.8025 |
Find the sum of numbers in the last column to get.
∑(xi−X bar )2= 3312.95
standard deviation = sqrt ( 3312.95 / 19 )
= 13.2048
standard deviation = 13.2048
( d ) coefficient of variation.= ( standard deviation / mean ) * 100
= (13.2048 / 47.05 ) * 100
= 28.07 %
coefficient of variation.= 28.07 %
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