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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 /渭尝 )

Frequency(f)

100-199

25

200-299

92

300-399

28

400-499

0

500-599

2

Short Answer

Expert verified

The computed mean of blood counts is 255.6(1000 cells / L).It is different from 255.1(1000 cells / L), the actual values.

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)

100-199

25

200-299

92

300-399

28

400-499

0

500-599

2

The actual measure of the mean of the blood platelet count of males is 255.1(1000 cells/L ).

02

Determine the midpoints of each class

The formula for midpoints using the upper and lower class limits is:

x=Upperlimit+Lowerlimit2

The formula for the mean of frequency distribution is:

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

Therefore, the values are tabulated as follows:

Blood Platelet Count of Males

(1000 cells /L)

Frequency

(f)

Lower limit

Upper limit

Midpoint

(x)

100-199

25

100

199

149.5

200-299

92

200

299

249.5

300-399

28

300

399

349.5

400-499

0

400

499

449.5

500-599

2

500

599

549.5

The mean is computed using the totals as follows:

Blood Platelet Count of Males

(1000 cells /L)

Frequency

(f)

Midpoint

(x)

fx

100-199

25

149.5

3737.5

200-299

92

249.5

22954

300-399

28

349.5

9786

400-499

0

449.5

0

500-599

2

549.5

1099

Totals:

f=147

fx=37576.5

Substitute the values in the formula to obtain:

x=37576.5147=255.6224

Thus, the mean blood platelet count of males is 255.6(1000 cells / L).

03

Compare the mean value with the actual mean value

The actual mean value is 255.1(1000 cells /L).

The tabulated or computed values are 255.6(1000 cells /L), which is different from 255.1, the actual value.

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

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