Find the mean, median and the mode of the following data: Weight (in Kg ) 42 47 52 57 62 67 72 Number of persons 3 8 6 8 11 5 9

Given: Weight (in Kg ) 42 47 52 57 62 67 72 Number of persons 3 8 6 8 11 5 9 To calculate the mean, median and mode: Weight (in Kg ) x i Number of persons F i Cumulative frequency x i F i 42 3 3 126 47 8 11 376 52 6 17 312 57 8 25 456 62 11 36 682 67 5 41 335 72 9 50 648 Total Σ F i = 50 Σ x i F i = 2935 Mean = Σ x i F i Σ F i = 2935 50 = 58 . 7 Kg Here the total number of observations ( n ) = 50 Median = 1 2 [ value of n 2 th term + value of n 2 + 1 th term ] Median = 1 2 [ value of 25 th term + value of 26 th term ] Median = 1 2 [ 57 + 62 ] = 119 2 = 59 . 5 Kg The highest frequency is 11 and the corresponding value of x i for the frequency 11 is 62 . Therefore, the mode is 62 . Hence, the mode is 62 Kg , median is 59 . 5 Kg and the mean is 58 . 7 Kg .

The following table shows the weight of 12 players: Weight (in kg ) 48 50 52 54 58 Number of players 4 3 2 2 1 Find the mean, median and mode.

Given: Weight (in kg ) 48 50 52 54 58 Number of players 4 3 2 2 1 To Calculate the mean, median and mode: Weight (in kg ) x i Number of players F i Cumulative frequency x i F i 48 4 4 192 50 3 7 150 52 2 9 104 54 2 11 108 58 1 12 58 Total ΣF i = 12 Σ x i F i = 612 Mean = Σx i F i ΣF i = 612 12 = 51 kg Here the total number of observation ( n ) = 12 Median = 1 2 [ value of n 2 th term + value of n 2 + 1 th term ] Median = 1 2 [ value of 6 th term + value of 7 th term ] Median = 1 2 [ 50 + 50 ] = 100 2 = 50 Kg Here the highest frequency is 4 and the corresponding value of x i is 48 . Mode = 48 Hence, the mean is 51 kg , median is 50 kg and mode is 48 kg.

E M B I B E

Tryout Maths A book on Mental Maths 7>Chapter 22 - Statistics>Exercise 63

S K Khanuja Solutions for Chapter: Statistics, Exercise 3: Exercise 63

Author:S K Khanuja

S K Khanuja Mathematics Solutions for Exercise - S K Khanuja Solutions for Chapter: Statistics, Exercise 3: Exercise 63

Attempt the free practice questions on Chapter 22: Statistics, Exercise 3: Exercise 63 with hints and solutions to strengthen your understanding. Tryout Maths A book on Mental Maths 7 solutions are prepared by Experienced Embibe Experts.