Measures of Central Tendency — Case-Study Based Question

On average, 80 patients get admitted into a nursing home in a day. The ages of the patients admitted and their number are as given below :

Find :

(i) The average age for which maximum cases occur.

(ii) The upper limit of modal class.

(iii) The mean of the given data.

Answer

(i) The average age for which maximum cases occur is the mode of the distribution.

The maximum frequency is 25, so the modal class is 30 - 40.

Here, l = 30, f₁ = 25, f₀ = 23, f₂ = 14 and h = 10.

By formula,

$\text{Mode} = l + \dfrac{f_1 - f_0}{2f_1 - f_0 - f_2} \times h \\[1em] = 30 + \dfrac{25 - 23}{2(25) - 23 - 14} \times 10 \\[1em] = 30 + \dfrac{2}{50 - 37} \times 10 \\[1em] = 30 + \dfrac{2}{13} \times 10 \\[1em] = 30 + \dfrac{20}{13} = 30 + 1.54 = 31.54.$

Hence, the average age for which maximum cases occur is 31.54 years (approx.).

(ii) The modal class is 30 - 40.

Hence, the upper limit of the modal class is 40.

(iii) Mean of the data :

By formula,

Mean = $\dfrac{Σfx}{Σf} = \dfrac{2550}{80}$ = 31.875 ≈ 31.88.

Hence, the mean of the given data is 31.88 years (approx.).

Along with an increase in population, electricity consumption per person is also increasing nationwide.

A survey is conducted for 560 families of Mangal Pande Nagar, Meerut. The following table gives the monthly consumption of electricity of these families.

Assuming that no family consumes more than 500 units of electricity, find :

(i) The mean monthly consumption.

(ii) The modal monthly class.

Answer

(i) Mean monthly consumption :

By formula,

Mean = $\dfrac{Σfx}{Σf} = \dfrac{110000}{560}$ = 196.43 (approx.).

Hence, the mean monthly consumption is 196.43 units (approx.).

(ii) The maximum frequency is 180, which corresponds to the class 200 - 300.

Hence, the modal monthly class is 200 - 300.