## RS Aggarwal Solutions Chapter 14 Statistics Ex 14G in PDF for Free Download

Contents

**Question 1.****Find the median of****(i) 2, 10, 9, 9, 5, 2,3,7, 11****(ii) 15,6, 16, 8,22,21,9, 18, 25****(iii) 20, 13, 18, 25, 6, 15, 21, 9, 16, 8, 22****(iv) 7, 4, 2, 5, 1, 4, 0, 10, 3, 8, 5, 9, 2****Solution:**

Arranging in ascending order, we get:

2,2,3,5,7,9,9,10,11

Here, number of terms is 9 which is odd.

∴ Median = th term = th term = 5th term = 7 Ans.

(ii) Arranging in ascending order, we get: 6, 8, 9, 15, 16, 18, 21, 22, 25

Here, number of terms is 9 which is odd.

∴ Median = th term = th term = 5th term = 16 Ans.

(iii) Arranging in ascending order, we get: 6, 8, 9, 13, 15, 16, 18, 20, 21, 22, 25

Here, number of terms is 11 which is odd.

∴ Median = th term = th term = 6th term = 16 Ans.

(iv) Arranging in ascending order, we get:

0, 1, 2, 2, 3, 4, 4, 5, 5, 7, 8, 9, 10

Here, number of terms is 13, which is odd.

Median = th term = th term = 7th term = 4 Ans.

**Question 2.****Find the median of****(i) 17, 19, 32, 10, 22, 21, 9, 35****(ii) 72, 63, 29, 51, 35, 60, 55, 91, 85, 82****(iii) 10, 75, 3, 15, 9, 47, 12, 48, 4, 81, 17,****Solution:**

Arranging in ascending order, we get 9, 10, 17, 19, 21, 22, 32, 35

Here, number of terms is 8 which is even

∴Median =

= [4th term + 5th term] = (19 + 21) = x 40 = 20

(ii) Arranging in ascending order, we get:

29, 35, 51, 55, 60, 63, 72, 82, 85, 91

Here number of terms is 10 which is even

∴Median =

= (60 + 63) = x 123 = 61.5 Ans.

(iii) Arranging in ascending order we get

3, 4, 9, 10, 12, 15, 17, 27, 47, 48, 75, 81

Here number of terms is 12 which is even.

∴Median =

= (6th term + 7th term) = (15 + 17)= x 32

= 16 Ans.

**Question 3.****The marks of 15 students in an examination are 25, 19, 17, 24, 23, 29, 31, 40, 19, 20, 22, 26, 17, 35, 21. Find the median score.****Solution:**

Arranging the given data in ascending order, we get :

17, 17, 19, 19, 20, 21, 22, 23, 24, 25, 26, 29, 31, 35, 40

∴ Median = th term = th term = 8th term = 23

∴ Median score = 23 Ans.

**Question 4.****The heights (in cm) of 9 girls are : 144.2, 148.5, 143.7, 149.6, 150, 146.5, 145, 147.3, 152.1. Find the median height.****Solution:**

Arranging in ascending order, we get:

143.7, 144.2, 145, 146.5, 147.3, 148.5, 149.6, 150, 152.1

Here, number of terms is 9 which is odd.

Median = th term = th term = 5th term = 147.3 cm

Hence, median height = 147.3 cm Ans.

**Question 5.****The weights (in kg) of 8 children are 13.4, 10.6, 12.7, 17.2, 14.3, 15, 16.5, 9.8. Find the median weight.****Solution:**

Arranging in ascending order, we get:

9.8, 10.6, 12.7, 13.4, 14.3, 15, 16.5, 17.2

Here number of terms is 8 which is even

∴Median =

= [4th term + 5th term]

= (13.4 + 14.3) = (27.7) = 13.85

∴ Median weight = 13.85 kg. Ans.

**Question 6.****The ages (in years) of 10 teachers in a school are : 32, 44, 53, 47, 37, 54, 34, 36, 40, 50.****Solution:**

Arranging in ascending order, we get:

32, 34, 36, 37, 40, 44, 47, 50, 53, 54

Here, number of terms is 10 which is even.

∴Median =

= [5th term + 6th term ] = (40 + 44) = x 84 = 42 .

∴ Median age = 42 years.

**Question 7.****If 10, 13, 15, 18, x + 1, x + 3, 30, 32, 35.41 are ten observations in an ascending order with median 24 find the value of x.****Solution:**

The given ten observations are 10, 13, 15, 18, x + 1, x + 3, 30, 32, 35, 41

These are even

∴Median =

= [5th term + 6th term ] = (x + 1 + x + 3) = (2x + 4)

= x + 2

But median is given = 24

∴ x + 2 = 24 => x = 24 – 2 = 22

Hence x = 22.

**Question 8.****Find the median weight for the following data :****Solution:**

Preparing the cumulative frequency table, we have:

Here, number of terms (n) = 41, which is odd,

Median = th term = th term = 21st term = 50 (∵ 20th to 28th term = 50)

Hence median weight = 50 kg Ans.

**Question 9.****Find the median for the following frequency distribution.****Solution:**

Arranging first in ascending order, we get:

Now preparing its cumulative frequency table

Here, number of terms is 37 which is odd.

Median = th term = th term = 19 th term = 22 (∵18th to 21st = 22)

Hence median – 22 Ans.

**Question 10.****Calculate the median for the following data****Solution:**

first arranging in ascending order we get

Now preparing its cumulative frequency table,we find:

Here, number of terms is 43, which if odd.

Median = th term = th term = 22nd term = 25 25 (∵ 11th to 26th = 25)

**Question 11.****The heights (in cm) of 50 students of a class are given below :****Find the median height****Solution:**

Arranging in ascending order,we get

Now preparing its cumulative frequency table, we find :

Here, number of terms = 50 which is even

∴Median =

= (154 + 155) = (309) = 154.5 (∵ 22nd to 25th = 154, 26th to 34th= 155)

**Question 12.****Find the median for the following data :****Solution:**

Arranging in ascending order, we get:

Now, preparing its cumulative frequency table.

Here, number of terms is 60 which is even

∴Median =

= (30th term + 31st term)

= (20 + 23) = x 43 = 21.5 (∵ 18th to 30th term = 20, 31st term to 34th = 23)

Hence median = 21.5 Ans.

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