The frequency distribution table below shows the mass, in grams, of 20 harvested oranges recorded during an agricultural experiment: | Mass (g) | Frequency (f) | |---|---| | 10 - 19 | 3 | | 20 - 29 | 5 | | 30 - 39 | 8 | | 40 - 49 | 4 | What is the mean mass of the harvested oranges?

The frequency distribution table below shows the mass, in grams, of 20 harvested oranges r… — JAMB UTME

The frequency distribution table below shows the mass, in grams, of $20$ harvested oranges recorded during an agricultural experiment:

What is the mean mass of the harvested oranges?

The mean mass of the harvested oranges is

31.0\text{ g}

The mean of grouped data is given by

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

. Finding the midpoints (

x

) of the intervals gives

14.5

24.5

34.5

, and

44.5

. Multiplying each midpoint by its frequency yields

43.5

122.5

276.0

, and

178.0

. The sum of these products is

620.0

, and dividing by the total frequency (

20

) gives

31.0\text{ g}

Determine the class midpoint (

x

) for each class interval.

Midpoints are:

\frac{10+19}{2} = 14.5

\frac{20+29}{2} = 24.5

\frac{30+39}{2} = 34.5

, and

\frac{40+49}{2} = 44.5

For grouped frequency data, each interval is represented by its central value (class mark or midpoint).

Multiply each midpoint (

x

) by its corresponding frequency (

f

) to calculate

fx

f_1 x_1 = 3 \times 14.5 = 43.5

f_2 x_2 = 5 \times 24.5 = 122.5

f_3 x_3 = 8 \times 34.5 = 276.0

f_4 x_4 = 4 \times 44.5 = 178.0

This computes the total mass contributed by the items in each interval.

Calculate the total sum of

fx

and total frequency

\sum f

\sum fx = 43.5 + 122.5 + 276.0 + 178.0 = 620.0

and

\sum f = 3 + 5 + 8 + 4 = 20

These sums are the numerator and denominator required for the mean formula.

Compute the mean using

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

\bar{x} = \frac{620.0}{20} = 31.0\text{ g}

Dividing the total weighted value by the total number of items gives the mean.

Calculating Mean for Grouped Frequency Data