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Chapter 3: Q30 (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 Actor when Oscar was won

Frequency

20鈥29

1

30鈥39

28

40鈥49

36

50鈥59

15

60鈥69

6

70鈥79

1

Short Answer

Expert verified

The mean value is computed as 44.5 years, which is not equal to the actual value.

Step by step solution

01

Given information

The frequency distribution for ages is as follows:

Age (in years) of Best Actor

when Oscar was won

Frequency

20鈥29

1

30鈥39

28

40鈥49

36

50鈥59

15

60鈥69

6

70鈥79

1

The actual mean using the original list is 44.1 years.

02

Determine the midpoints of each class

The formula for the mean of frequency distribution is:

x炉=鈭f脳x鈭f....1

Here,

f represents the frequencies.

x denotes the midpoints of the classes.

The formula for determining the midpoints:

x=Upperlimit+Lowerlimit2

Compute midpoints for each class interval as follows:

Age (in years) of Best Actor

when Oscar was won

Frequency

(f)

Lower limit

Upper limit

Midpoint

(x)

20鈥29

1

20

29

24.5

30鈥39

28

30

39

34.5

40鈥49

36

40

49

44.5

50鈥59

15

50

59

54.5

60鈥69

6

60

69

64.5

70鈥79

1

70

79

74.5

The computation for the sum totals is done as follows:

Age (in years) of Best Actor

when Oscar was won

Frequency

(f)

Midpoint

(x)

f脳x

20鈥29

1

24.5

24.5

30鈥39

28

34.5

966

40鈥49

36

44.5

1602

50鈥59

15

54.5

817.5

60鈥69

6

64.5

387

70鈥79

1

74.5

74.5

Totals:

鈭f=87

鈭f脳x=3871.5

Substituting the values in the equation (1), you get:

x炉=3871.587=44.5

Thus, the mean age is computed as 44.5 years.

03

Compare the mean value with the actual mean value

The actual mean value is known to be 44.1 years.

The actual mean value is different from the one tabulated from the frequency distribution; that is, 44.5 years.

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20鈥29

29

30鈥39

34

40鈥49

14

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3

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1

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