In Exercises 29–32, 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 /$\mathbf{\mu L}$ )	Frequency(f)
100-199	25
200-299	92
300-399	28
400-499	0
500-599	2

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

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

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

$x=\frac{\text{Upper}\text{limit}+\text{Lower}\text{limit}}{2}$

The formula for the mean of frequency distribution is:

$\overline{x}=\frac{\sum \left(f\times x\right)}{\sum f}$, where fdenotes the frequencies and xdenotes the midpoints of the classes.

Therefore, the values are tabulated as follows:

The mean is computed using the totals as follows:

Substitute the values in the formula to obtain:

$$\begin{gathered} \overline{x}=\frac{37576.5}{147} \\ =255.6224 \end{gathered}$$

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

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

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

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