Ex 14.2, 4 - Chapter 14 Class 10 Statistics

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Ex 14.2, 4 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. Mode = l + (𝑓1 −𝑓0)/(2𝑓1 −𝑓0 −𝑓2) × h Modal class = Interval with highest frequency = 30 – 35 where l = lower limit of modal class h = class-interval f1 = frequency of the modal class f0 = frequency of class before modal class f2 = frequency of class after modal class Mode = l + (𝑓1 −𝑓0)/(2𝑓1 −𝑓0 −𝑓2) × h = 30 + (10 −9)/(2(10) − 9 − 3) × 5 = 30 + 1/(20 −12) × 5 = 30 + 5/8 = 30 + 0.625 = 30.625 Number of students / 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 Mean(𝑥 ̅) = a + h × (∑▒𝑓𝑖𝑢𝑖)/(∑▒𝑓𝑖) Where a = assumed mean h = Class interval = 20 − 15 = 5 & ui = (𝑥𝑖 −𝑎)/ℎ ∑▒𝑓𝑖 = 35 ∑▒𝑓𝑖𝑢𝑖 = -58 Mean(𝑥 ̅) = a + h × (∑▒𝑓𝑖𝑢𝑖)/(∑▒𝑓𝑖) Mean(𝑥 ̅) = 37.5 + 5 × (−58)/35 Mean(𝑥 ̅) = 37.5 - 58/7 𝑥 ̅ = 37.5 – 8.286 𝑥 ̅ = 29.214 ∴ Mean = 𝑥 ̅ = 29.214 Thus, most states have student-teacher ratio 30.625 (mode), And average student-teacher ratio is 29.214 (mean)