Answer
Median = 57
Q1=51
Q3=68
IQR= 17
The value 54 lies in relation to second quartile.
b. 60th percentile = 61 hours
Approximately 60% of these 18 randomly selected managers worked for less than or equal to 61 hours last week.
c. Percentile rank of 64= 66.67%
There are about 66.67% of these 18 randomly selected managers worked for less than 64 hours last week.
Work Step by Step
a. The ranked data in increasing order is as follows:
45,45,48,49,50,52,54,55,56,56,58,61,63,64,66,70,74,77,79
Median = $(56+58)/2$ = 57
Q1=$(50+52)/2$ =51
Q3=$(66+70)/2$ =68
IQR= Q3-Q1 = $(68-51)$ = 17
The value 54 lies in relation to second quartile because it is larger than first quartile but smaller than third quartile.
b. percentile = $(Kxn)/ 100 $=$( 60 x 18)/100 $=$10.8\approx 11th term$
60th percentile = 11th term = 61 hours
Approximately 60% of these 18 randomly selected managers worked for less than or equal to 61 hours last week.
c. There are 12 values that are less than 64.
Percentile rank of 64= $\frac{12}{18} \times 100% $= 66.67%
About 66.67% of these 18 randomly selected managers worked for less than 64 hours last week.
