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Chapter 3: Q29 (page 95)

In Exercises 29鈥32, find the mean of the data summarized in the frequency distribution. Also, compare the computed means to the actual means obtained by using the original list of data values, which are as follows: (Exercise 29) 36.2 years; (Exercise 30) 44.1 years; (Exercise 31) 224.3; (Exercise 32) 255.1..

Age (year) of Best Actress when Oscar was won

Frequency

20鈥29

29

30鈥39

34

40鈥49

14

50鈥59

3

60鈥69

5

70鈥79

1

80鈥89

1

Short Answer

Expert verified

The mean value is computed as 36.2 years, which is equal to the actual value.

Step by step solution

01

Given information

The frequency distribution is given as follows:

Age (year) of Best Actress

when Oscar was won

Frequency

20鈥29

29

30鈥39

34

40鈥49

14

50鈥59

3

60鈥69

5

70鈥79

1

80鈥89

1

The actual measure of mean is 36.2 years.

02

Determine the midpoints of each class

The mean for the frequency distribution is obtained using the formula

x炉=鈭f脳x鈭f, where fdenotes the frequencies and xrepresents the midpoints of the classes.

The midpoints x are computed for a class interval as follows:

x=Upperlimit+Lowerlimit2

Therefore, the values are tabulated as follows:

Age (in years) of Best Actress

when Oscar was Won

Frequency

(f)

Lower limit

Upper limit

Midpoint

(x)

20鈥29

29

20

29

24.5

30鈥39

34

30

39

34.5

40鈥49

14

40

49

44.5

50鈥59

3

50

59

54.5

60鈥69

5

60

69

64.5

70鈥79

1

70

79

74.5

80鈥89

1

80

89

84.5

03

The mean for the values is computed using the formula

The computation for the sum totals is done as follows:

Age (in years) of Best Actress

when Oscar was Won

Frequency

(f)

Midpoint

(x)

f脳x

20鈥29

29

24.5

710.5

30鈥39

34

34.5

1173

40鈥49

14

44.5

623

50鈥59

3

54.5

163.5

60鈥69

5

64.5

322.5

70鈥79

1

74.5

74.5

80鈥89

1

84.5

84.5

Totals:

鈭f=87

鈭f脳x=3151.5

Substituting the values in the formula, you get:

x炉=3151.587=36.2241

Thus, the mean age of the best actress when Oscar was won is 36.2 years.

04

Compare the mean value with the actual mean value

The actual mean value is the same as the one computed from the frequency distribution; that is, 36.2 years.

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