The table below shows the distribution of heights (in cm) of 20 potted plants recorded during a biology experiment: | Height (cm) | Frequency (f) | | :--- | :--- | | 10 – 14 | 4 | | 15 – 19 | 6 | | 20 – 24 | 8 | | 25 – 29 | 2 | What is the mean height of the potted plants?

The table below shows the distribution of heights (in cm) of 20 potted plants recorded dur… — JAMB UTME

The table below shows the distribution of heights (in cm) of $20$ potted plants recorded during a biology experiment:

What is the mean height of the potted plants?

The mean height of the potted plants is

19\text{ cm}

The mean height is calculated by multiplying each class interval's midpoint by its frequency, summing these products (

380

), and dividing by the total number of plants (

20

), giving

19\text{ cm}

Calculate the midpoint (

x

) for each class interval.

Class midpoints are

12

17

22

, and

27

The midpoint represents the estimated mean value of data items in a grouped class interval.

Multiply each midpoint (

x

) by its corresponding frequency (

f

) to find

f \cdot x

4 \times 12 = 48

6 \times 17 = 102

8 \times 22 = 176

, and

2 \times 27 = 54

This determines the total estimated sum of values for each class.

Sum all

f \cdot x

values and calculate the total frequency

\sum f

\sum fx = 48 + 102 + 176 + 54 = 380

and

\sum f = 4 + 6 + 8 + 2 = 20$.

These totals are required for the grouped mean formula.

Compute the mean using the formula

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

\bar{x} = \frac{380}{20} = 19\text{ cm}$.

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

Grouped Mean Calculation using Class Midpoints

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