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 = $\frac{15+10+25+19+10+17}{6}=16$

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

$\frac{ (15-16)^{2} + (10-16)^{2}+ (25-16)^{2}+ (19-16)^{2}+ (10-16)^{2}+ (17-16)^{2} }{6}$
$\frac{1+36+81+9+36+1}{6}= \frac{164}{6} =27.333...$

Standard deviation = $\sqrt{27.333...}=5.23$ (rounded to 2 dp)