Question

Help !! with a big points!

An office manager recorded the number of reams of paper that were used for a printer each month for six months: 15, 10, 25, 19, 10, 17.
(a) Identify the five-number summary of the data set.
(b) Draw the box-and-whisker plot.
(c) Compute the standard deviation. Show all your work.

Answer 1

Part (a)

Mean =
`(15+10+25+19+10+17)/(6)=16`

Range = 25 - 10 = 15

Median,
`Q_(2)` = 16 (Refer to the first picture)

Lower Quartile,
`Q_(1)` = 10

Upper Quartile,
`Q_(3)` = 22

Interquartile Range, IQR =
`Q_(3)- Q_(1)=22-10=12`

Part (b)

The box plot is shown in the second picture below

Part (c)

Mean = 16

Subtracting 16 from each data value, find sum of the square of each answer and divide by 6


`( (15-16)^(2) + (10-16)^(2)+ (25-16)^(2)+ (19-16)^(2)+ (10-16)^(2)+ (17-16)^(2) )/(6)`

`(1+36+81+9+36+1)/(6)= (164)/(6) =27.333...`

Standard deviation =
`√(27.333...)=5.23` (rounded to 2 dp)