The frequency distribution table below shows the number of books checked out daily at a public library over a period of 40 days: | Number of Books | Number of Days (f) | |---|---| | 1 - 5 | 4 | | 6 - 10 | 10 | | 11 - 15 | 16 | | 16 - 20 | 10 | What is the mean number of books checked out per day?

The frequency distribution table below shows the number of books checked out daily at a pu… — JAMB UTME

The frequency distribution table below shows the number of books checked out daily at a public library over a period of $40$ days:

What is the mean number of books checked out per day?

The mean number of books checked out per day is

12.0

The correct answer of

12.0

is found by calculating the midpoint (

x

) for each class interval (

3, 8, 13, 18

), multiplying each midpoint by its respective frequency to find

f \cdot x

, summing these products to obtain

\sum fx = 480

, and dividing by the total frequency

\sum f = 40

Determine the midpoint (

x

) for each class interval.

Midpoints:

x_1 = \frac{1+5}{2} = 3

x_2 = \frac{6+10}{2} = 8

x_3 = \frac{11+15}{2} = 13

x_4 = \frac{16+20}{2} = 18

Grouped data calculations require a single representative value (the midpoint) for each class interval.

Calculate the product of frequency and midpoint (

f \cdot x

) for each class interval.

f_1 x_1 = 4 \times 3 = 12

f_2 x_2 = 10 \times 8 = 80

f_3 x_3 = 16 \times 13 = 208

f_4 x_4 = 10 \times 18 = 180

This yields the total value contributed by each class interval.

Calculate total frequency (

\sum f

) and total sum of products (

\sum fx

\sum f = 4 + 10 + 16 + 10 = 40

, and

\sum fx = 12 + 80 + 208 + 180 = 480

These sums are needed to compute the weighted mean.

Apply the grouped mean formula

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

\bar{x} = \frac{480}{40} = 12.0

Dividing the sum of all values by the total frequency yields the grouped mean.

Grouped Mean Calculation