Exercises 13.2

EX 13.2 (Question: 4)

📅 Published: 15 June, 2025 🕒 Read: 0 min

EX 13.2 (Question: 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.
Solution: Mode we use the formula: Mode, =𝒍+[(𝒇_𝟏−𝒇_𝟎)/(𝟐𝒇_𝟏−𝒇_𝟎−𝒇_𝟐 )]×𝒉 Where: 𝑙 = 30→ lower boundary of modal class (30 – 35) 𝑓1 = 10 → frequency of modal class 𝑓0 = 9 → frequency of class before modal class 𝑓2 = 3 → frequency of class after modal class ℎ = 5 → class width
Now substitute: "Mode "=30+((10−9)/(2(10)−9−3))×5 =30+(1/(20−12))×5 =30+(1/8)×5 =30+0.625 =30.63
Mean We use the Assumed Mean Method: Let the assumed mean a = 30
Using Mean Formula: Mean, 𝒙 ‾=𝒂+((∑1▒ 𝒇_𝒊 𝒖_𝒊)/(∑1▒ 𝒇_𝒊 )) 𝑥 ‾=30+((−27.5)/35) =30−0.7857 =𝟐𝟗.𝟐𝟏 Mean = 29.21 students per teacher Mode = 30.63 students per teacher

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