The following table shows the age distribution of cases of certain disease reported during a year in a particular city.

Obtain the mean, median and mode of the above data.

We have

For Mean:

Mean is given by

⇒ [from the table]

⇒ Mean = 32.1

For Median:

Here, we get total frequency, ∑f_i = N = 50. So,

Since, N/2 = 25. Mark a cumulative frequency which is just greater than 25.

Here, it is 29. So, median class would be 24.5 – 34.5.

Median is given by

Where, l = lower limit of the median class = 24.5

N/2 = 25 (as calculated above)

m = cumulative frequency of the class preceding the median class = 17

f = frequency of the median class = 12

c = width of the median class = 10

Putting all these values in the formula, we get

⇒

⇒ Median = 24.5 + 6.67 = 31.167

For Mode:

We have the following data in exclusive type in tabular form. We can interpret the column ‘No. of cases’ as frequency.

Note that, highest frequency = 12

Corresponding class interval = 24.5 – 34.5

⇒ Modal class = 24.5 – 34.5

Mode is given by,

Where, l = lower limit of the modal class = 24.5

f = frequency of the modal class = 12

f₁ = frequency of the class preceding the modal class = 11

f₂ = frequency of the class succeeding the modal class = 10

c = width of the class interval = 10

Putting all these values in the modal formula,

⇒

⇒

⇒ Mode = 24.5 + 3.33

⇒ Mode = 27.83

Thus, mean is 32.1, median is 32.167 and mode is 27.83.