The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and mode of the data and compare them.

Let’s draw a table showing midpoints, frequencies and cumulative frequency.

For median:

We have, total frequency, N = 68

N/2 = 68/2 = 34

Observe, cf = 42 is just greater than 34.

Thus, median class = 125-145

Median is given by

Where,

L = Lower class limit of median class = 125

N/2 = 34

cf = cumulative frequency of the class preceding median class = 22

f = frequency of the median class = 20

h = class interval of the median class = 20

Substituting these values in the formula of median, we get

⇒ Median = 125 + 12

⇒ Median = 137

For mean:

Mean is given by

⇒

⇒ Mean = 135 + 2.06

⇒ Mean = 137.06

For mode:

Here, highest frequency is 20.

So, the modal class = 125-145

Mode is given by

Where,

L = Lower class limit of the modal class = 125

h = class interval of the modal class = 20

f₁ = frequency of the modal class = 20

f₀ = frequency of the class preceding the modal class = 13

f₂ = frequency of the class succeeding the modal class = 14

Substituting values in the formula of mode,

⇒

⇒ Mode = 125 + 10.76

⇒ Mode = 135.76

Thus, median is 137, mean is 137.06 and mode is 135.76.

Median and mean, both gives us the average value of a data, with just the difference that mean can give us quantitative measure only but median can give us both quantitative as well as qualitative measure of a data. And that is why, mean and median have come out to be very close in this question.

Mode gives the value that appears most in a given data. Thus, the maximum monthly consumption of electricity is 135.76.