Approximate the population variance given the following frequency distribution.
$\begin{array} { c c }
\hline \text { Class } & \text { Frequency } \
\hline 0 - 19 & 19 \
20 - 39 & 11 \
40 - 59 & 13 \
60 - 79 & 15 \
80 - 99 & 19 \
\hline
\end{array}$
A)923.6
B)30.6
C)935.8
D)30.4

Question

Approximate the population variance given the following frequency distribution.
 $\begin{array} { c c } 
\hline \text { Class } & \text { Frequency } \
\hline 0 - 19 & 19 \
20 - 39 & 11 \
40 - 59 & 13 \
60 - 79 & 15 \
80 - 99 & 19 \
\hline
\end{array}$
A)923.6
B)30.6
C)935.8
D)30.4

Quizplus · Accepted Answer

To approximate the population variance from a frequency distribution, we first need to calculate the mean (average) of the data. We do this by finding the midpoint of each class, multiplying each midpoint by the class frequency, summing these products, and then dividing by the total number of data points.Midpoints: - For 0-19: (0+19)/2 = 9.5- For 20-39: (20+39)/2 = 29.5- For 40-59: (40+59)/2 = 49.5- For 60-79: (60+79)/2 = 69.5- For 80-99: (80+99)/2 = 89.5Multiplying each midpoint by its frequency and summing:- (9.5 * 19) + (29.5 * 11) + (49.5 * 13) + (69.5 * 15) + (89.5 * 19) = 180.5 + 324.5 + 643.5 + 1042.5 + 1700.5 = 3891Total number of data points:- 19 + 11 + 13 + 15 + 19 = 77Mean (average):- 3891 / 77 = 50.5325Next, we calculate the variance by using the formula for the variance of a frequency distribution, which involves taking each midpoint, subtracting the mean, squaring the result, multiplying by the frequency, summing these products, and then dividing by the total number of data points.Variance calculation:- Sum[((midpoint - mean)^2 * frequency)] / total number of data points- This involves a bit of calculation, but after performing these steps, you would find that the variance approximates to 923.6, which is option A.

Approximate the Population Variance Given the Following Frequency Distribution A)9236 B)30

Approximate the Population Variance Given the Following Frequency Distribution A)9236
B)30