Sir how i solve this statistics chapter question of exercise 14.2 of question no.3 of class 10th, give me the best and simple way to solve this problem 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:
Given data:
Modal class = 1500-2000,
l = 1500,
Frequencies:
fm = 40 f1 = 24, f2 = 33 and
h = 500
Mode formula:
Mode = l+ [(fm-f1)/(2fm-f1-f2)]×h
Substitute the values in the formula, we get
Mode =1500+[(40-24)/(80-24-33)]×500
Mode = 1500+((16×500)/23)
Mode = 1500+(8000/23) = 1500 + 347.83
Therefore, modal monthly expenditure of the families = Rupees 1847.83
Calculation for mean:
First find the midpoint using the formula, xi =(upper limit +lower limit)/2
Let us assume a mean, A be 2750
The formula to calculate the mean,
Mean = x̄ = a +(∑fiui /∑fi)×h
Substitute the values in the given formula
= 2750+(-35/200)×500
= 2750-87.50
= 2662.50
So, the mean monthly expenditure of the families = Rupees 2662.50