Calculate the median for the following data: Height cm 160 150 152 161 156 154 155 Number of Students 12 8 4 4 3 3 7

Let us arrange the marks in ascending order and prepare the following data: Height cm Number of students f Cumulative frequency c f 150 8 8 152 4 12 154 3 15 155 7 22 156 3 25 160 12 37 161 4 41 Here N = 41 Median = size of N + 1 2 th value = size of 41 + 1 2 th value = size of 21 st value. If the 41 students were arranged in order (of height), the 21 st student would be the middle most one, since there are 20 students on either side of him/her. We therefore need to find the height against the 21 st student. 15 students (see cumulative frequency) have height less than or equal to 154 cm . students have height less than or equal to 155 cm . This means that the 21 st student has a height 155 cm . Therefore, Median = 155 cm

The following table gives the weekly expenditure of 200 families. Find the median of the weekly expenditure. Weekly expenditure ₹ 0 - 1000 1000 - 2000 2000 - 3000 3000 - 4000 4000 - 5000 Number of families 28 46 54 42 30

Weekly Expenditure Number of families f Cumulative frequency c f 0 - 1000 28 28 1000 - 2000 46 74 2000 - 3000 54 128 3000 - 4000 42 170 4000 - 5000 30 200 N = 200 Median class = N 2 th value = 200 2 th value = 100 th value Median class = 2000 - 3000 N 2 = 100 , l = 2000 m = 74 , c = 1000 , f = 54 Median = l + N 2 - m f × c = 2000 + 100 - 74 54 × 1000 = 2000 + 26 54 × 1000 = 2000 + 481 . 5 = 2481 . 5 Hence, the required median is 2481 . 5 .

The Median of the following data is 24 . Find the value of x . Class Interval C I 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 Frequency f 6 24 x 16 9

Class Interval C I Frequency f Cumulative frequency c f 0 - 10 6 6 10 - 20 24 30 20 - 30 x 30 + x 30 - 40 16 46 + x 40 - 50 9 55 + x N = 55 + x Since the median is 24 and median class is 20 - 30 l = 20 N = 55 + x , m = 30 , c = 10 , f = x Median = l + N 2 - m f × c 24 = 20 + 55 + x 2 - 30 x × 10 24 - 20 = 55 + x - 60 2 x × 10 4 = x - 5 2 x × 10 4 = 5 x - 25 x (after simplification) 4 x = 5 x - 25 5 x - 4 x = 25 x = 25 Hence, the required value of x is 25 .

Find the mode for the following data. Marks 1 - 5 6 - 10 11 - 15 16 - 20 21 - 25 Number of students 7 10 16 32 24

Marks f 0 . 5 - 5 . 5 7 5 . 5 - 10 . 5 10 10 . 5 - 15 . 5 16 15 . 5 - 20 . 5 32 20 . 5 - 25 . 5 24 Modal class is 16 - 20 since it has the maximum frequency. l = 15 . 5 , f = 32 , f 1 = 16 , f 2 = 24 , c = 20 . 5 - 15 . 5 = 5 Mode = l + f - f 1 2 f - f 1 - f 2 × c = 15 . 5 + 32 - 16 64 - 16 - 24 × 5 = 15 . 5 + 16 24 × 5 = 15 . 5 + 3 . 33 = 18 . 83 Hence, the required mode is 18 . 83 .