Question

Calculate the mode from the following data: 

x	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50
f	10	20	18	32	21

Answer 1

1. Identify the modal class

The modal class is the class interval with the highest frequency. In this dataset, the maximum frequency is 32, which corresponds to the class interval 30 – 40.

2. Note the required values

From the modal class and surrounding data, we identify the following values for the formula:

l (Lower limit of the modal class) = 30

f₁ (Frequency of the modal class) = 32

f₀ (Frequency of the preceding class) = 18

f₂ (Frequency of the succeeding class) = 21 

h (Class width/size) = 10

3. Apply the mode formula

The formula for the mode of grouped data is:

Mode = `l + ((f_1 - f_0)/(2f_1 - f_0 - f_2)) xx h`

Substitute the values into the formula:

Mode = `30 + ((32 - 18)/(2(32) - 18 - 21)) xx 10`

4. Solve the calculation

Simplify the expression step-by-step:

Mode = `30 + (14/(64 - 39)) xx 10`

Mode = `30 + (14/25) xx 10`

Mode = 30 + (0.56 × 10)

Mode = 30 + 5.6

Mode = 35.6

The final mode of the given data is 35.6.