Question

A social scientist measures the number of minutes (per day) that a small hypothetical population of college students spends online.

Student	Score	Student	Score
A	99	F	54
B	81	G	96
C	89	H	71
D	92	I	92
E	89	J	33

(a) What is the range of data in this population?
min

(b) What is the IQR of data in this population?
   min

(c) What is the SIQR of data in this population?
   min

(d) What is the population variance?


(e) What is the population standard deviation? (Round your answer to two decimal places.)
min

Answer 1

(a) Range of data

The range is the difference between the largest and smallest value of the population.

Range = Largest observation - smallest observation = 99 - 33 = 66 min

(b) IQR (Inter-quartile range)

The formula to find the IQR is Q3 - Q1

Q3 - upper quartile, Q1 - lower quartile

Arrange the observations in increasing order.

The observations in increasing order are, 33, 54, 71, 81, 89, 89, 92, 92, 96, 99

Q1 - the median of first-half data = 71

Q3 - the median of second-half data = 92

IQR = Q3 - Q1 = 92 - 71 = 21 min

(c) SIQR (Semi-interquartile range)

The formula of SIQR is,

SIQR = IQR / 2 = 21 / 2 = 10.5

SIQR = 10.5 min

(d) Population variance

The formula of population variance is,

X - data values

The formula to find the mean(average) is,

Population variance = 403.24

(e) Population standard deviation

Square root of variance is nothing but standard deviation

Population standard deviation = Square root of 403.24 = 20.08

Population standard deviation = 20.08