The following table represents the marks secured by a batch of 12 students in science and social studies tests: Serial no 1 2 3 4 5 6 7 8 9 10 11 12 Science 25 72 28 60 30 46 32 54 65 33 53 48 Social Studies 67 28 48 55 25 60 27 49 43 23 41 20 By calculating the median, identify the subject in which the level of achievement is higher.

The table representing the marks secured by a batch of 12 students in science and social studies tests is given below: Serial no 1 2 3 4 5 6 7 8 9 10 11 12 Science 25 72 28 60 30 46 32 54 65 33 53 48 Social Studies 67 28 48 55 25 60 27 49 43 23 41 20 The median is the middle value of a set of observations arranged in either ascending or descending order. Method to find the median: (i) Arrange the given data in ascending or descending order of magnitude. (ii) Determine the total number of observations, say, n . (iii) If n is odd, then median = value of n + 1 2 th observation (iv) If n is even, then median = average of n 2 th and n 2 + 1 th observations We shall find the median marks obtained by the students both for Science and Social Studies. The level of achievement is higher for the subject for which the median is higher. For both the subjects, n = 12 , which is even. We have, n 2 = 12 2 = 6 and n 2 + 1 = 12 2 + 1 = 6 + 1 = 7 Median for Science Arranging the marks obtained in Science, we obtain, 25 , 28 , 30 , 32 , 33 , 46 , 48 , 53 , 54 , 60 , 65 , 72 . The 6 th observation is 46 and the 7 th observation is 48 . The average of 46 and 48 is 46 + 48 2 = 94 2 = 47 So, the median marks obtained for Science is 47 . Median for Social Studies Arranging the marks obtained in Social Studies, we obtain, 20 , 23 , 25 , 27 , 28 , 42 , 43 , 48 , 49 , 55 , 60 , 67 . The 6 th observation is 42 and the 7 th observation is 43 . The average of 42 and 43 is 42 + 43 2 = 85 2 = 42 . 5 So, the median marks obtained for Social Studies is 42 . 5 . We have, 47 > 42 . 5 . So, the median marks obtained by the students for Science is higher. Therefore, the level of achievement is higher in Science.

E M B I B E

Be a Maths Star>Chapter 18 - Data Handling>Exercise 18.4>Q 1

HARD

7th ICSE

IMPORTANT

Earn 100

Find the median of the following.

$28, 35, 32, 26, 27, 35, 36, 28, 29, 32, 37, 24, 33, 26, 25, 31, 22, 36, 27$

50% studentsanswered this correctly

Important Questions on Data Handling

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7th ICSE

IMPORTANT

Be a Maths Star>Chapter 18 - Data Handling>Exercise 18.4>Q 2

Find the median of the first ten prime numbers.

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7th ICSE

IMPORTANT

Be a Maths Star>Chapter 18 - Data Handling>Exercise 18.4>Q 3

A total of

15

students secured the following marks in a test in statistics:

35, 29, 23, 11, 30, 17, 18, 10, 29, 19, 20, 13, 28, 25, 17

Find the median marks.

HARD

7th ICSE

IMPORTANT

Be a Maths Star>Chapter 18 - Data Handling>Exercise 18.4>Q 4

The following table represents the marks secured by a batch of $12$ students in science and social studies tests:

Serial no	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$	$12$
Science	$25$	$72$	$28$	$60$	$30$	$46$	$32$	$54$	$65$	$33$	$53$	$48$
Social Studies	$67$	$28$	$48$	$55$	$25$	$60$	$27$	$49$	$43$	$23$	$41$	$20$