Question

A social scientist measures the number of minutes (per day) that a small hypothetical population of college students spends online.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	61	F	76
B	86	G	92
C	94	H	81
D	86	I	29
E	95	J	95

(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. The range is the difference between the highest and lowest values in the data set.

Ordering the data from least to greatest, we get:

29   61   76   81   86   86   92   94   95   95   

The lowest value is 29.

The highest value is 95.

The range = 95 - 29 = 66.

b. The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the bottom half.

29   61   76   81   86   86   92   94   95   95   

So, the bottom half is

29   61   76   81   86   

The median of these numbers is 76.

The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the upper half.

29   61   76   81   86   86   92   94   95   95   

So, the upper half is

86   92   94   95   95   

The median of these numbers is 94.

The interquartile range is the difference between the third and first quartiles.

The third quartile is 94.

The first quartile is 76.

The interquartile range = 94 - 76 = 18.

c.

d. Sample mean is

Create the following table.

data	data-mean	(data - mean)2
61	-18.5	342.25
86	6.5	42.25
94	14.5	210.25
86	6.5	42.25
95	15.5	240.25
76	-3.5	12.25
92	12.5	156.25
81	1.5	2.25
29	-50.5	2550.25
95	15.5	240.25

Find the sum of numbers in the last column to get.

So population variance is

e. Now population standard deviation is