Approximate the population variance given the following frequency distribution.

$\begin{array} { c c }
\hline \text { Class } & \text { Frequency } \
\hline 0 - 14 & 12 \
15 - 29 & 16 \
30 - 44 & 15 \
45 - 59 & 9 \
60 - 74 & 11 \
\hline
\end{array}$

A) 20.3
B) 413.3
C) 419.9
D) 20.5

Question

Approximate the population variance given the following frequency distribution.

$\begin{array} { c c } 
\hline \text { Class } & \text { Frequency } \
\hline 0 - 14 & 12 \
15 - 29 & 16 \
30 - 44 & 15 \
45 - 59 & 9 \
60 - 74 & 11 \
\hline
\end{array}$

A) 20.3
B) 413.3
C) 419.9
D) 20.5

Quizplus · Accepted Answer

To approximate the population variance from a frequency distribution, we first need to calculate the midpoint of each class, multiply each midpoint by the class frequency to find the total for each class, and then use the formula for variance. The midpoint of each class is found by averaging the upper and lower bounds of each class. The midpoints are 7, 22, 37, 52, and 67 for each class respectively. The total of all frequencies is 63. The approximate mean (x̄) is found by summing the products of midpoints and frequencies and dividing by the total frequency: $\frac{(7*12) + (22*16) + (37*15) + (52*9) + (67*11)}{63}$. The next step is to calculate the sum of squared deviations from the mean, which involves squaring the difference between each class midpoint and the mean, multiplying by the class frequency, summing these products, and finally dividing by the total number of observations. This calculation gives us the variance. The detailed calculation is omitted, but following this procedure with the given frequencies and midpoints yields a variance of approximately 413.3.

Approximate the Population Variance Given the Following Frequency Distribution A) 203 B) 413

Approximate the Population Variance Given the Following Frequency Distribution A) 203
B) 413