A random sample of weights (in carats) of sapphires in a jeweler's collection is shown. Fi the mean of the sample.
$\begin{array} { c c } \text { Class Boundaries } & \text { Frequency } \ 0.95 - 2.95 & 10 \ 2.95 - 4.95 & 15 \ 4.95 - 6.95 & 10 \ 6.95 - 8.95 & 10 \ 8.95 - 10.95 & 9 \end{array}$
A) 10.80
B) 5.55
C) 5.95
D) 5.69

Question

Quizplus · Accepted Answer

The mean of a grouped data set can be estimated by using the formula:Mean = (sum of (midpoint of each class * frequency of each class)) / total frequencyThe midpoint of each class is the average of the lower and upper class boundaries.For the given data, the midpoints and frequencies are:Class Boundaries | Midpoint | Frequency0.95 - 2.95 | 1.95 | 102.95 - 4.95 | 3.95 | 154.95 - 6.95 | 5.95 | 106.95 - 8.95 | 7.95 | 108.95 - 10.95 | 9.95 | 9Mean = (1.95*10 + 3.95*15 + 5.95*10 + 7.95*10 + 9.95*9) / 64= 5.69Therefore, the mean of the sample is 5.69 carats.

A Random Sample of Weights (In Carats) of Sapphires in a Jeweler's