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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..

Blood Platelet Count of Males (1000 cells / )

Frequency(f)

0-99

1

100-199

51

200-299

90

300-399

10

400-499

0

500-599

0

600-699

1

Short Answer

Expert verified

The mean value computed from the table is 224.1 (1000 cells / L), which is different from the actual value of 224.3 (1000 cells /L ).

Step by step solution

01

Given information

The distribution of frequencies of the blood platelet count of males is as follows:

Blood Platelet Count of Males (1000 cells /L )

Frequency(f)

0-99

1

100-199

51

200-299

90

300-399

10

400-499

0

500-599

0

600-699

1

The actual measure of the mean of the blood platelet count for males is 224.3(1000 cells/L ).

02

Determine the midpoints of each class

The midpoint x is computed using the class limits as follows:

x=Upperlimit+Lowerlimit2

Therefore, the mean is computed from the frequency distribution by the formula:

x=fxf, where frepresents the frequencies and xdenotes the midpoints of the classes.

Therefore, the values are tabulated as follows:

Blood Platelet Count of

Males (1000 cells / )

Frequency

(f)

Lower limit

Upper limit

Midpoint

(x)

0-99

1

0

99

49.5

100-199

51

100

199

149.5

200-299

90

200

299

249.5

300-399

10

300

399

349.5

400-499

0

400

499

449.5

500-599

0

500

599

549.5

600-699

1

600

699

649.5

The mean is computed using the totals as follows:

Blood Platelet Count of Males

(1000 cells / L)

Frequency

(f)

Midpoint

(x)

fx

0-99

1

49.5

49.5

100-199

51

149.5

7624.5

200-299

90

249.5

22455

300-399

10

349.5

3495

400-499

0

449.5

0

500-599

0

549.5

0

600-699

1

649.5

649.5

Totals:

f=153

fx=34273.5

Substituting the values in the formula, you get:

x=34273.5153=224.0098

Thus, the mean blood platelet count of males is 224.1(1000 cells / L).

03

Compare the mean value with the actual mean value

Compare it to the computed mean value. The actual mean value is almost the same as the computed mean of 224.1 (1000 cells / ).

Thus, the actual mean value is different from the one computed from the frequency distribution.

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