Question

Q1. Find the mean of :
i. 7, 10, 4 and 17
ii. 7, 5, 0, 3, 0 , 6, 0, 9, 1, and 4
iii. 2.1, 4,5, 5.2, 7.1 and 9.3
Q2. Find the mean of :
i. First eight natural numbers
ii. All prime numbers upto 30
Q3. Heights ( in cm) of 7 boys of a locality are 144cm , 155 cm, 168cm, 163 cm, 167 cm, 151 cm and 158 cm. Find their mean height.
Q4. The mean of 18 , 28 , x , 32, 14 and 36 is 23. Find the value of x.

Answer 1

SOLUTION :

• Formula of calculating Mean :-

$\: \: \bigstar \: \: \: \large{\boxed{ \bold{ \: Mean = \dfrac{Sum \: \: of \: \: the \: \: observation}{No. \: \: of \: \: observation}}}} \:$

______________________________

[1]

• (i) To find the mean of : 7, 10, 4 and 17

$\sf{\therefore \: \: Required \: \: mean = \dfrac{Sum \: \: of \: \: the \: \: observation}{No. \: \: of \: \: observation}} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ = \frac{7 + 10 + 4 + 17}{4}} \\ \\ \sf{ = \frac{38}{4}} \: \: \: \\ \\ \sf{ = 9.5} \: \: \:$

• Hence, the mean of 10, 4 and 17 is 9.5

______________________

• (ii) To find the mean of : 7, 5, 0, 3, 0 , 6, 0, 9, 1, and 4

$\sf{\therefore \: \: Required \: \: mean = \dfrac{Sum \: \: of \: \: the \: \: observation}{No. \: \: of \: \: observation}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ = \frac{7 + 5 + 0 + 3 + 0 + 6 + 0 + 9 + 1 + 4}{10}} \\ \\ \sf{ = \frac{35}{10}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf{ = 3.5} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

• Hence, the mean of 7, 5, 0, 3, 0 , 6, 0, 9, 1, and 4 is 3.5

______________________

• (iii) To find the mean of : 2.1, 4,5, 5.2, 7.1 and 9.3

$\sf{\therefore \: \: Required \: \: mean = \dfrac{Sum \: \: of \: \: the \: \: observation}{No. \: \: of \: \: observation}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ = \frac{2.1 + 4.5 + 5.2 + 7.1 + 9.3}{5}} \\ \\ \sf{ = \frac{28.2}{5}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf{ = 5.64} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

• Hence, the mean of : 2.1, 4,5, 5.2, 7.1 and 9.3 is 5.64

______________________________

[2]

• (i) To find the mean of : First eight natural numbers

The first eight natural numbers are :- 1, 2, 3, 4, 5, 6, 7, 8

$\sf{\therefore \: \: Required \: \: mean = \dfrac{Sum \: \: of \: \: the \: \: observation}{No. \: \: of \: \: observation}} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ = \frac{1 + 2 + 3 + 4 + 5 + 6 + 7 + 8}{8}} \\ \\ \sf{ = \frac{36}{8}} \: \: \: \: \:\\ \\ \sf{ = 4.5} \: \: \: \: \: \:$

• Hence, the mean of first eight natural numbers is 4.5

______________________

• (ii) To find the mean of : All prime numbers upto 30

The prime numbers upto 30 are : 2, 3, 5, 7, 11, 13, 17, 19, 23, 29

$\sf{\therefore \: \: Required \: \: mean = \dfrac{Sum \: \: of \: \: the \: \: observation}{No. \: \: of \: \: observation}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ = \frac{2 + 3 + 5 + 7+ 11 + 13 + 17 + 19 + 23 + 29}{10}} \\ \\ \sf{ = \frac{129}{10}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf{ = 12.9} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

• Hence, the mean of all prime numbers upto 30 is 12.9

______________________________

[3]

• To find the mean of : The height of the boys.

The observation are : 144cm , 155 cm, 168cm, 163 cm, 167 cm, 151 cm and 158 cm

• Sum of the observation = 1106 cm

• No. of observation = 7

$\sf{\therefore \: \: Required \: \: mean = \dfrac{Sum \: \: of \: \: the \: \: observation}{No. \: \: of \: \: observation}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf{ = \frac{1106 \: cm}{7}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf{ = 158 \: cm} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

• Hence, the mean of the height of the boys is 158 cm.

______________________________

[4]

Given :-

• The observation are : 18 , 28 , x , 32, 14 and 36

• The mean of the observation : 23

• The no. of observation : 6

To Find :-

• The value of x = ?

According to question,

$\: \: \bigstar \: \: \: \sf{ \: Mean = \frac{Sum \: \: of \: \: the \: \: observation}{No. \: \: of \: \: observation}}$

$\sf{ \implies \: 23 = \frac{18 + 28 + x + 32 + 14 + 36}{6}}$

$\sf{ \implies \: 23 = \frac{128 + x}{6}}$

$\sf{ \implies \: 128 + x = 23 \times 6}$

$\sf{ \implies \: 128 + x = 138}$

$\sf{ \implies \: x = 138 - 128}$

$\: \: \: \: \sf{\therefore \: \: x = 10}$

• Hence, the value of x is 10.