Question

Every year, colleges and universities collect data on their entering class. Below are the writing scores for entering college freshman:

64.5, 43.7, 56.7, 56.7, 46.3, 64.5, 39.1, 39.1, 51.5, 64.5,
56, 41.1, 59.3, 51.5, 65.1, 59.3, 56.7, 54.1, 43, 56.7,
54.1, 47.6, 48.9, 48.9, 54.1, 64.5, 33.3, 38.5, 67.1, 59.3, 61.9

a)
mean =  

b)
min =  

c)
max =  

d)
range =  

e)
variance =  

f)
SD =  

Answer 1

a) mean = sum of all data points÷ no of data points

=1646.7 ÷21

=53.14

b)min = min value =33.3

c) maximum value = 67.1

d)range = max value - min value

67.1 - 33.3 = 33.8

e)

x x-xbar (x - xbar)²

56	2.66	7.085
41.1	-12.23	149.77
59.3	5.96	35.54
51.5	-1.83	3.37
65.1	11.76	138.34
59.3	5.96	35.54
56.7	3.36	11.30
54.1	0.76	0.58
43	-10.33	106.87
56.7	3.36	11.30
54.1	0.76	0.58
47.6	-5.73	32.92
48.9	-4.43	19.69
48.9	-4.43	19.69
54.1	0.76	0.58
64.5	11.16	124.58
33.3	-20.038	401.52
38.5	-14.83	220.16
67.1	13.76	189.38
59.3	5.96	35.54
61	7.66	58.70

variance =

= 1603.16 ÷20

= 80.15 approx

f) standard deviation =

=

= 8.95