## ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 15 Data Handling Ex 15.5

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) Arrange the data in ascending order

We get, 1, 3, 3, 4, 5, 5, 6

∴ Median = \(\left(\frac{n+1}{2}\right)^{t h}\) term

= \(\left(\frac{7+1}{2}\right)^{\text { th }}\) = 4^{th} term

(ii) After arranging data, we get

1, 3, 3, 4, 5, 5, 6, 6

∴ Median = \(\frac{4+5}{2}=\frac{9}{2}=4 \cdot 5\)

Question 2.

Calculate the mean, the median and the mode of the numbers :

1, 3, 2, 6, 2, 3, 1, 3

Solution:

(a) Mean = \(\frac{1+3+2+6+2+3+1+3}{8}\)

= \(\frac{21}{8}\) = 2.625

Hence mean = 2.625

(b) Arranging the given data in ascending order, we get

1, 1, 2, 2, 3, 3, 3,6

Total number of observations (items) = 8 (even).

There are two middle items : – 2 and 3.

Their average = \(\frac{2+3}{2}=\frac{5}{2}=2 \cdot 5\)

Hence the median of the given numbers = 2.5.

(c) In the given numbers,

3 is repeated more number of time than any other number.

∴ Mode = 3.

Question 3.

Calculate the mean, the median and the mode of the following numbers :

3, 7, 2, 5, 3, 4, 1, 5, 3, 6

Solution:

(a) Mean = \(\frac{3+7+2+5+3+4+1+5+3+6}{10}=\frac{39}{10}=3 \cdot 9\)

Hence the mean = 3.9

(b) Arranging the given data in ascending order, we get,

1, 2, 3, 3, 3, 4, 5, 5, 6, 7

Total numbers of obvervations (items) = 10 (even)

There are two middle items – 3 and 4

Their average = \(\frac{3+4}{2}=\frac{7}{2}=3 \cdot 5\)

Hence the median of the given numbers = 3.5

(c) In the given numbers 3 is repeated more than any other number

∴ Mode = 3