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 84 F 92 B 37 G 87 C 92 H 95 D 61 I 96 E 87 J 74 (a) What is the range of data in this population? min (b) What is the IQR of data in this population? (c) What is the SIQR of data in this population? (d) What is the population variance? (e) What is the population standard deviation? (Round your answer to two decimal places.)

Answer 1

Answer)

Given data is

84, 92, 37, 87, 92, 95, 61, 96, 87, 74

A)

First we need to arrange this data in ascending order

37, 61,74, 84, 87, 87,92, 92,95, 96

Range = highest number - lowest number = 96 - 37 = 59

B)

IQR = Q3 - Q1

Q3 is the middlemost number of second half = 92

Q1 is the middlemost number of first half = 74

IQR = 92 - 74 = 18

C)

SIQR = IQR/2 = 9

D)

to find variance

First we need to find mean

Mean = (sum of the observations)/(number of observations)

Mean = (37 + 61..)/10 = 80.5

Now we need to subtract this mean from each and every observation and then we need to take the square and add them

(37-80.5)^2 + (61 - 80.5)^2 .... = 3126.5

Now we need to divide this by n

Variance = 3126.5/10 = 312.65

E)

S.d = √variance = 17.6819116613