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