Question

1. Find the standard​ deviation, s, of sample data summarized in the frequency distribution table given below by using the formula​ below, where x represents the class​ midpoint, f represents the class​ frequency, and n represents the total number of sample values.​ Also, compare the computed standard deviation to the standard deviation obtained from the original list of data​ values 9.0

s=∑f•x2−∑(f•x)2n(n−1)

Interval	30​-36	37​-43	44​-50	51​-57	58​-64	65​-71
Frequency	2	17	39	19	10	1

Standard deviation = ?

​(Round to one decimal place as​ needed.)

2. Heights of men on a baseball team have a​ bell-shaped distribution with a mean of 170 cm and a standard deviation of 5 cm. Using the empirical​ rule, what is the approximate percentage of the men between the following​ values?

a.---------​% of the men are between 160 cm and 180 cm.

b.----------​%of the men are between 155 cm and 185 cm.

Answer 1

(1)

From the given data, the following Table is calculated:

Class	Frequency (f)	Mid point (x)	f x	f x2
30 - 36	2	33	66	2178
37 - 43	17	40	680	27200
44 - 50	39	47	1833	86151
51 - 57	19	54	1026	55404
58 - 64	10	61	610	37210
65 - 71	1	68	68	4624
Total =	n = = 88

Sample Standard Deviation (s) is given by:

So,

Standard Deviation = 7.0

(2)

(a)

= 170

= 5

X = 160

So,

Z = (160 - 170)/5

= - 2

X = 180

So,

Z = (180 - 170)/5

=2

So,

Using empirical rule:

95.45 % of the men are between 160 cm and 180 cm.

(b)

= 170

= 5

X = 155

So,

Z = (155 - 170)/5

= - 3

X = 185

So,

Z = (185 - 170)/5

= 3

So,

Ubsing empirical rule:

99.73 % of the men are between 155 cm and 185 cm.