The following distribution gives the state-wise teacher-student ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures
No of Students per teacher - Number of states / U.T
15-20 → 3
20-25 → 8
25 - 30 → 9
30 - 35 → 10
35 - 40 → 3
40 - 45 → 0
45 - 50 → 0
50 - 55 → 2
Modal class = 30 – 35,
l = 30,
Class width (h) = 5,
fm = 10, f1 = 9 and f2 = 3
Mode Formula:
Mode = l + [(fm-f1)/(2fm-f1-f2)] × h
Substitute the values in the given formula
Mode = 30 + ((10 - 9)/(20 - 9 - 3)) × 5
Mode = 30 + (5/8) = 30 + 0.625
Mode = 30.625
Therefore, the mode of the given data = 30.625
Calculation of mean:
Find the midpoint using the formula, xi = (upper limit +lower limit)/2
Mean = x̄ = ∑fixi /∑fi
= 1022.5/35
= 29.2
Therefore, mean = 29.2