The table below records the daily water consumption, in liters, of 40 households in a residential community: | Daily Water Consumption (liters) | Frequency (f) | | :--- | :--- | | 10 - 19 | 6 | | 20 - 29 | 10 | | 30 - 39 | 14 | | 40 - 49 | 7 | | 50 - 59 | 3 | Calculate the mean daily water consumpti

The table below records the daily water consumption, in liters, of 40 households in a resi… — JAMB UTME

The table below records the daily water consumption, in liters, of $40$ households in a residential community:

Daily Water Consumption (liters)	Frequency ( $f$ )
$10 - 19$	$6$
$20 - 29$	$10$
$30 - 39$	$14$
$40 - 49$	$7$
$50 - 59$	$3$

Calculate the mean daily water consumption for this community in liters.

Answer: 32.25 liters

The mean daily water consumption is

32.25

liters.

The mean of a grouped frequency distribution is computed using the formula

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

, where

x

represents the midpoint of each class interval and

f

is the class frequency. Calculating the midpoints yields

14.5, 24.5, 34.5, 44.5, 54.5

. Multiplying each midpoint by its frequency gives products of

87, 245, 483, 311.5, 163.5

, which sum to

1290

. Dividing

1290

by the total frequency of

40

yields

32.25

liters.

Find the class midpoint (

x

) for each interval by taking the average of the upper and lower limits of each class.

Midpoints are

14.5

24.5

34.5

44.5

, and

54.5

For grouped data, the midpoint serves as the representative value for all data within that class interval.

Compute the product of frequency and midpoint (

f \cdot x

) for each class interval.

Products are

87

245

483

311.5

, and

163.5

This accounts for the total sum contributed by each group.

Sum all products

\sum f x

and divide by the total number of households

\sum f = 40

\text{Mean} = \frac{1290}{40} = 32.25.

The formula for the estimated mean of grouped data is

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

Grouped Mean Estimation using Class Midpoints