SChand Composite Mathematics Class 7 Chapter 15 Data Handling Exercise 15A

  Exercise 15 A

Question 1 

Find the mean of : 

(a) First 5 natural number 

Sol: $\bar{x}=\frac{1+2+3+4+5}{5}=\frac{15}{5}=3$

(b) First 7 whole numbers

Sol: $\bar{x}=\frac{0+1+2+3+4+5+6}{7}=\frac{21}{7}=3$

(c) First 4 prime number 

Sol: $\bar{x}=\frac{2+3+5+7}{4}=\frac{17}{4}=4.25$

(d) Rs7, Rs 19 , Rs 31, Rs 43, Rs 70

Sol: $\bar{x}=\frac{7+19+31+43+70}{5}=\frac{170}{5}=Rs 34$

Question 2

Seema obtained the following scores (Out of 100) $80,85,90,71,60,100$ . What is her mean score? 

Sol: $\bar{x}=\frac{80+85+90+71+60+100}{6}=\frac{486}{6}=81$

Question 3

Shaleen's last six batting scores were 138, 144, 155 ,142, 167,172. What was his mean score? 

Sol: $\bar{x}=\frac{138+144+155+142+167+172}{6}$

$\bar{x}=\frac{918}{6} =\bar{x}=153$

Question 4

Madhu worked $2 \frac{1}{2}$ hours on Monday, $3 \frac{1}{4}$ hrs. on Tuesday, and $2 \frac{3}{4}$ hrs. on Wednesday. What is the mean number of hours she worked on these three days?

Sol: Total number of hours worked = $2 \frac{1}{2}+3 \frac{1}{4}+2 \frac{3}{4}$

$=\frac{5}{2}+\frac{13}{4}+\frac{11}{4}$

$=\frac{10+13+11}{4}=\frac{34}{4}$

Mean $\bar{x}=\frac{\text { Sun of observation}}{\text { Number of observation }}$

$=\frac{\frac{34}{4}}{3}=\frac{34}{12}=\frac{17}{6}=2 \frac{5}{6}$ hours

Question 5

Ayushree sat for six tests and ananya sat for seven tests. Their percentage scores were: 

$\begin{array}{|l|c|c|c|c|c|c|c|}\hline \text { Ayushree } & 68 & 75 & 70 & 45 & 57 & 77 & \\\hline \text { Ananya } & 52 & 87 & 64 & 531 & 74 & 81 & 86 \\\hline\end{array}$

Sol: Mean of ayushree = $\frac{68+75+70+45+57+77}{6}$

$=\frac{392}{6}=65.33$

Mean of ananya = $\frac{52+87+64+53+74+81+86}{7}$

$=\frac{497}{7}=71$

Ananya > Ayushree

Question 6

Find the mean of first ten odd natural numbers 

Sol: $=\frac{1+3+5+7+9+11+13+15+17+19}{10}$

$=\frac{100}{10}=10$

Question 7

If the mean of 16, 14, x ,23 ,20  is 18 . find the value  of x 

Sol: $18=\frac{16+14+x+23+20}{5}$

$90=x+73 \Rightarrow x=90-73$

$x=17$ Ans 

Question 8

If the mean of x, x+ 2, x+4 ,x+6 , x+8 is 24, find x 

Sol: $24=\frac{x+x+2+x+4+x+6+x+8}{5}$

$120=5 x+20 \Rightarrow 120-20=5 x$

$\Rightarrow 100=5 x$

$\Rightarrow x=\frac{100}{5} \Rightarrow x=20$ answer

Question 9

Nisha secured 73,86,78 and 75 marks in four tests. What is the least number of marks she can secure in her next test, if she has to have a mean score of 80 marks in five test? 

Sol: Let the number =x 

$80=\frac{73+86+78+75+x}{5}$

$400=312+x=x=400-312$

$x=88$ marks

Question 10

The mean of 6 numbers is 24. If one number is excluded, the mean of remaining numbers becomes 22 find the excluded number . 

Sol: Mean = $\frac{Sum of observation}{No. of Observation }$

$24=\frac{5.0}{6} \Rightarrow 5.0 \cdot=144$

22 = $\frac{Sum of obs of 5 No}{No. of obs}$

$22=\frac{5.0}{5}$

$110=5.0$

Excluded No. = 144-110= 34 answer