The table below shows the distribution of masses (in kg) of 50 bags of cement inspected at a building construction site: | Mass (kg) | Frequency (f) | | :--- | :--- | | 40 - 44 | 5 | | 45 - 49 | 12 | | 50 - 54 | 18 | | 55 - 59 | 15 | Calculate the mean mass of the bags of cement in kg.

The table below shows the distribution of masses (in kg) of 50 bags of cement inspected at… — JAMB UTME

The table below shows the distribution of masses (in kg) of $50$ bags of cement inspected at a building construction site:

Calculate the mean mass of the bags of cement in kg.

Answer: 51.3 kg

The mean mass of the cement bags is 51.3 kg.

The mean mass of grouped data is computed using the formula

\bar{x} = \frac{\sum fx}{\sum f}

, where

x

represents the class midpoints and

f

represents the frequency of each class. The class midpoints are

42

47

52

, and

57

. Multiplying these midpoints by their respective frequencies yields

210

564

936

, and

855

. Summing these values gives

\sum fx = 2565

. Dividing by the total frequency

\sum f = 50

produces a mean mass of

\frac{2565}{50} = 51.3\text{ kg}

Determine the midpoint (x) of each class interval

Midpoints are 42, 47, 52, and 57

For grouped data, the class midpoint represents the average value of all observations falling within that class interval.

Calculate the product of each midpoint and its corresponding frequency (fx)

Products are 210, 564, 936, and 855

Multiplying the midpoint by frequency gives the total estimated mass contributed by that class interval.

Sum all frequencies and all fx products

Total frequency sum = 50, Total product sum = 2565

These totals are required to calculate the weighted average across all intervals.

Divide the sum of fx by the total frequency

Mean = 51.3 kg

Applying the formula for grouped mean: Mean = (sum of fx) / (sum of f).

Grouped Data Mean Calculation