Exercise 1.80 asks you to calculate the seven deviations from Example 1.32, square them, and find s' and s directly from the deviations. Working one or two short examples by hand helps you understand how the standard deviation is obtained. In practice, you will use either software or a calculator that will find s.

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My question for my stats homework comes from the textbook Introduction to the Practice of Statistics Ninth Edition.  This comes from section exercise 1.80. from the textbook, my professor wants me to caluate using the three columns. Can you help me slove this problem for me? 

Metabolic rate. A person's metabolic rate is the rate at which the body con-
sumes energy. Metabolic rate is important in studies of weight gain, dieting
and exercise. Here are the metabolic rates of seven men who took part in
a study of dieting. (The units are calories per 24 hours. These are the same
calories used to describe the energy content of foods.)
EXAMPLE 1.32
In
METABOL
1792 1666 1362 1614 1460 1867 1439
Enter these data into your calculator or software and verify that
x 1600 calories
s = 189.24 calories
Figure 1.16 plots these data as dots on the calorie scale, with their mean
marked by an asterisk (*). The arrows mark two of the deviations from the
mean. If you were calculating s by hand, you would find the first deviation as
%3D
X1-x = 1792- 1600= 192
%3D
Transcribed Image Text:Metabolic rate. A person's metabolic rate is the rate at which the body con- sumes energy. Metabolic rate is important in studies of weight gain, dieting and exercise. Here are the metabolic rates of seven men who took part in a study of dieting. (The units are calories per 24 hours. These are the same calories used to describe the energy content of foods.) EXAMPLE 1.32 In METABOL 1792 1666 1362 1614 1460 1867 1439 Enter these data into your calculator or software and verify that x 1600 calories s = 189.24 calories Figure 1.16 plots these data as dots on the calorie scale, with their mean marked by an asterisk (*). The arrows mark two of the deviations from the mean. If you were calculating s by hand, you would find the first deviation as %3D X1-x = 1792- 1600= 192 %3D
1.3 Describing Distributions with Numbers
39
X = 1439
X = 1600
x = 1792
deviation = -161
deviation = 192
1300
1400
1500
1600
1700
1800
1900
Metabolic rate
FIGURE 1.16 Metabolic rates for seven men, with the mean (*) and the deviations of
two observations from the mean, Example 1.32.
Exercise 1.80 asks you to calculate the seven deviations from Example 1.32,
square them, and find s and s directly from the deviations. Working one or two
short examples by hand helps you understand how the standard deviation is
obtained. In practice, you will use either software or a calculator that will find s.
,2
Transcribed Image Text:1.3 Describing Distributions with Numbers 39 X = 1439 X = 1600 x = 1792 deviation = -161 deviation = 192 1300 1400 1500 1600 1700 1800 1900 Metabolic rate FIGURE 1.16 Metabolic rates for seven men, with the mean (*) and the deviations of two observations from the mean, Example 1.32. Exercise 1.80 asks you to calculate the seven deviations from Example 1.32, square them, and find s and s directly from the deviations. Working one or two short examples by hand helps you understand how the standard deviation is obtained. In practice, you will use either software or a calculator that will find s. ,2
Expert Solution
Step 1

Given Information:

Data represents the metabolic rates of seven men who took part in a study of dieting.

1792   1666    1362    1614    1460    1867    1439

We are asked to calculate the seven deviations, square them and find s2 and s:

Mean is the sum of observations divided by the total number of observations:

x¯=1792+1666+1362+1614+1460+1867+14397=1600

Now, find each of the deviations xi-x¯ and their squares:

1792-1600=192

1666-1600=66

1362-1600=-238

1614-1600=14

1460-1600=-140

1867-1600=267

1439-1600=-161

Square of the deviations are:

1792-16002=36864

(1666-1600)2=4356

(1362-1600)2=56644

(1614-1600)2=196

(1460-1600)2=19600

(1867-1600)2=71289

(1439-1600)2=25921

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