## ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 17 Data Handling Ex 17.3

Question 1.

Find the median of the following data:

(i) 3, 1, 5, 6, 3, 4, 5

(ii) 3, 1, 5, 6, 3, 4, 5, 6

Solution:

(i) 3, 1, 5, 6, 3, 4, 5

Arranging in ascending order, 1, 3, 3, 4, 5, 5, 6

Here, N = 7 which is odd

Median = \(\frac { 7+1 }{ 2 }\) th term = 4th term = 4

(ii) 3, 1, 5, 6, 3, 4, 5, 6

Arranging in ascending order, 1, 3, 3, 4, 5, 5, 6, 6

Here, N = 8 which is even

Question 2.

Find the mode of the following data:

(i) 3, 1, 5, 6, 3, 4, 5, 3

(ii)

Marks obtained | 15 | 17 | 20 | 22 | 25 |

Number of students | 6 | 17 | 12 | 18 | 13 |

Solution:

(i) 3, 1, 5, 6, 3, 4, 5, 3

Arranging in order, 1, 3, 3, 3, 4, 5, 5, 6

Here, 3 comes maximum times

Mode = 3

(ii)

Marks obtained | 15 | 17 | 20 | 22 | 25 |

Number of students | 6 | 17 | 12 | 18 | 13 |

Here, 22 comes maximum times

Mode = 18

Question 3.

Find the median and the mode of the data:

13, 16, 12, 14, 19, 12, 14, 13, 14

Solution:

13, 16, 12, 14, 19, 12, 14, 13, 14

Arranging in ascending order, 12, 12, 13, 13, 14, 14, 14, 16, 19

(i) Median = \(\frac { 9+1 }{ 2 }\) th = \(\frac { 10 }{ 2 }\) th = 5th term = 14

(Here n = 9 which is odd)

(ii) 14 comes maximum times

Mode = 14

Question 4.

The scores in mathematics test (out of 25) of 15 students is as follows:

19, 25, 23, 20, 9, 20, 15, 10, 5, 16, 25, 20, 24, 12, 20

Find the mode and median of this data. Are the same?

Solution:

19, 25, 23, 20, 9, 20, 15, 10, 5, 16, 25, 20, 24, 12, 20

Arranging in ascending order, 5, 9, 10, 12, 15, 16, 19, 20, 20, 20, 20, 23, 24, 25, 25

Here, N = 15 which is odd

(i) Median = \(\frac { 15+1 }{ 2 }\) th term = 8th term = 20

Mode = 20 comes maximum times

Mode = 20

Yes, they are same.

Question 5.

The weights (in kg) of 15 students of a class are:

38, 42, 35, 37, 45, 50, 32, 43, 43, 40, 36, 38, 43, 38, 47

(i) Find the median and mode of this data.

(ii) Is there more than one mode?

Solution:

38, 42, 35, 37, 45, 50, 32, 43, 43, 40, 36, 38, 43, 38, 47

Arranging in ascending order, 32, 35, 36, 37, 38, 38, 38, 40, 42, 43, 43, 43, 45, 47, 50

Here n = 15 which is odd

Median = \(\frac { 15+1 }{ 2 }\) th = 8th term = 40

Mode : 38 and 43 have come maximum times

Mode is 38 or 43

Yes, there is more than one mode : 38 and 43

Question 6.

The runs scored in a cricket match by 11 players is as follows:

6, 15, 120, 50, 100, 80, 10, 15, 8, 10, 15

Find the mean, mode and median of this data. Are the three same?

Solution:

6, 15, 120, 50, 100, 80, 10, 15, 8, 10, 15

Arranging in ascending order, 6, 8, 10, 10, 15, 15, 15, 50, 80, 100, 120

Here n = 11 which is odd

(ii) Median = \(\frac { 11+1 }{ 2 }\) th term = 6 th term = 15

(iii) Mode : 15 comes maximum times

Mode = 15

No, the three are not same, only median and mode are same.

Question 7.

Find the mode of the following data:

12, 14, 12, 15, 16, 13, 14, 18, 19, 12, 14, 15, 16, 15, 16, 16, 15, 17, 13, 16, 16, 15, 15, 13, 15, 17, 15, 14, 15, 13, 15, 14.

Solution:

We see that the frequency of 15 is the maximum.

Mode = 15