The following data gives the distribution of total monthly household expenditure of 200 families of a village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure :

Expenditure (in ₹)	Number of families
1000 - 1500	24
1500 - 2000	40
2000 - 2500	33
2500 - 3000	28
3000 - 3500	30
3500 - 4000	22
4000 - 4500	16
4500 - 5000	7

By formula,

Mode = l + $\Big(\dfrac{f$1 - f0}{2f1 - f0 - f_2}\Big) \times h

Here,

1. Class size is h.

2. The lower limit of modal class is l

3. The Frequency of modal class is f₁.

4. Frequency of class preceding modal class is f₀.

5. Frequency of class succeeding the modal class is f₂.

Class 1500 - 2000 has the highest frequency.

∴ It is the modal class.

∴ l = 1500, f₁ = 40, f₀ = 24, f₂ = 33 and h = 500.

Substituting values we get :

$\text{Mode} = 1500 + \Big(\dfrac{40 - 24}{2 \times 40 - 24 - 33}\Big) \times 500 \\[1em] = 1500 + \dfrac{16}{80 - 57} \times 500 \\[1em] = 1500 + \dfrac{16}{23} \times 500 \\[1em] = 1500 + \dfrac{8000}{23} \\[1em] = 1500 + 347.83 \\[1em] = 1847.83$

We will find mean using step deviation method.

By formula,

Mean = a + $\dfrac{Σf$iui}{Σf_i} \times h

Substituting values we get :

$\text{Mean } = 3250 + \dfrac{-235}{200} \times 500 \\[1em] = 3250 - \dfrac{1175}{2} \\[1em] = 3250 - 587.5 \\[1em] = 2662.50$

Hence, mean = ₹ 2662.50 and mode = ₹ 1847.83.