Example 6 - Chapter 14 Class 10 Statistics

Transcript

Example 6 The marks distribution of 30 students in a mathematics examination are given in Table 14.3 of Example 1. Find the mode of this data. Also compare and interpret the mode and the mean. Class interval Number of students 10 – 25 2 25 – 40 3 40 – 55 7 55 – 70 6 70 – 85 6 85 – 100 6 Mode = l + (𝑓1 −𝑓0)/(2𝑓1 −𝑓0 −𝑓2) × h Modal class = Interval with highest frequency = 40 – 55 where l = lower limit of modal class=40 h = class-interval= 25 – 10 = 15 f1 = frequency of the modal class=7 f0 = frequency of class before modal class=3 f2 = frequency of class after modal class=6 Mode = l + (𝑓1 −𝑓0)/(2𝑓1 −𝑓0 −𝑓2) × h = 40 + (7 −3)/(2(7)−3−6) × 15 = 40 + 4/(14 −9) × 15 = 40 + 4/5 × 15 = 40 + 4 × 3 = 40 + 12 = 52 ∴ Mode = 52 So, maximum number of students obtained 52 marks & Mean = 62 (From Example 1) Therefore, on an average, the students got 62 marks.