Exercise 15 A
Question 1
Ans: (a) first $s$ natural numbers are 1,2,3,4,5
$\text { So } \begin{gathered}\text { Mean }=\frac{1+2+3+4+5}{5}=\frac{15}{5}\left\{\bar{x}=\frac{\sum x_{1}}{n}\right\} \\=3\end{gathered}$
(b) first 7 whole numbere are $0,1,2,3,4,5,6$
$\begin{aligned}&\text { So } \text { mean }=\frac{0+1+2+3+4+5+6}{7} \\&\left\{\begin{array}{l}\left\{x=\frac{\sum x_{1}}{n}\right\} \\=\frac{21}{7}=3\end{array}\right.\end{aligned}$
(C) First 4 prime numbers are $2,3,5,7$
$\text { So } \begin{aligned}\text { mean }=\frac{2+3+5+7}{4} &=\frac{17}{4} \quad\left\{\bar{x}=\frac{\sum x_{1}}{n}\right\}\\&=4.25\end{aligned}$
(d) $1.3 \mathrm{~cm}, 5.7 \mathrm{~cm}, 9.8,6.4 \mathrm{~cm}, 6.9 \mathrm{~cm}$
So mean $=\frac{1.3+5.7+9.8+6.4+6.9}{5} \quad\left\{\bar{x}=\frac{\sum x_{1}}{n}\right\}$
$=\frac{30.1}{5}=6.02 \mathrm{~cm}$
(e) Rs. 7, Rs. 19, Rs. 31, Rs 43, Rs. 70
so $\operatorname{mean}=\frac{7+19+31+43+70}{5} \quad\left\{\bar{x}=\frac{\sum x_{1}}{n}\right\}$
$=\frac{170}{5}=$ Rs 34
Question 2
Ans: Score obtained are $80,85,90,71,60,100$
So
$\begin{aligned}&\text { mean }=\frac{80+85+90+71+60+100}{6} \\&=\frac{486}{6}=81\end{aligned}$
Question 3
Ans: Lat 6 batting score $138,144,155,142,167,172$ So mean score
$\begin{aligned}&=\frac{138+144+155+1+2+167+172}{6} \quad\left\{\bar{x}=\frac{\Sigma x_{1}}{n}\right\} \\&=\frac{918}{6}=153\end{aligned}$
Question 4
Ans: Working hours from Monday to Wednesday
for 3 days $=2 \frac{1}{2}, 3 \frac{1}{4}$ and $2 \frac{3}{4}$
So mean nour $=\frac{2 \frac{1}{2}+3 \frac{1}{4}+2 \frac{3}{4}}{3}=\frac{8 \frac{1}{2}}{3}$
$=\frac{17}{2 \times 3}=\frac{17}{6}$ hours $=2 \frac{5}{6}$ hours
Question 5
Ans: Ayushree's score $=\frac{68,75,70,45,57,77}{6}$
$\left\{\bar{x}=\frac{\sum x}{n}\right\}$
$=\frac{392}{6}=65 \frac{1}{3} \%$
and Ananya's score (in percent)
$=52,87,64,53,74,81,86$
So Her mean $=\frac{52+87+64+53+74+81+86}{7}$
$=\frac{497}{7}=71 \%$
Question 6
Sol: first 10 odd natural number are
$1,13,5,7,9,11,13,115,17,19$
So
$\begin{aligned}\operatorname{mean} &=\frac{1+3+5+7+9+11+13+15+17+19}{10} \\&=\frac{100}{10}=10\end{aligned}$
Question 7
Sol: mean of 5 herms $=18$
So Then total $=18 \times 5=90$
But sum of given numbers is
$=16+14+x+23+20=73+x$
So $73+x=90 \Rightarrow x=90-73=17$
Hence $x=17$
Question 8
Ans : Mean of 5 terms = 24
So their total =$24 \times 5=120$
now Sum of mean= $x+x+2+x+4+x+6+x+8$ =5x + 20
So $5 x+20=120 \Rightarrow 5 x=120-20$
$\Rightarrow 5 x=100 \Rightarrow x=\frac{100}{5}=20$
So $x=20$
Question 9
Ans: Madhu practiced on her sitar for 45 minutes , 30 min, 60min, 50min and 20 min
So her mean practice
$\frac{45+30+60+50+20}{5} \quad\left\{\bar{x}=\frac{\sum x_{1}}{n}\right\}$
$=\frac{205}{5}=41 \mathrm{~min}$
Question 10
Ans: Marks secured by Nisha in 4 test are = 73, 86,78,75
Let she secured marks in the next fifth test
Then mean marks secured will be
$=\frac{73+86+78+75+x}{5}=\frac{312+x}{5}$
But her mean score=80 marks
So $\frac{312+x}{5}=80 \Rightarrow 312+x=400$
$\Rightarrow x=400-312=88$
Hence her score in the fifth test = 88 marks
Question 11
Ans: mean score of a cricketer $=60$ run
No of innings $(n)=10$
So Total runs $=60 \times 10=600$ runs
mean score in 11 innings $=62$
So Total runs $=62 \times 11=682$ run
So No of runs scored in 11 th innings
$=682-600=82 \text { runs }$
Question 12
Ans: (IMAGE TO BE ADDED)
$\begin{aligned} \operatorname{mean}(\bar{x}) &=\frac{\varepsilon f i x i}{\sum f i} \\=\frac{1600}{50} &=32 \mathrm{~kg} \end{aligned}$
Question 13
(IMAGE TO BE ADDED)
So mean $=\frac{\sum f_{i x i ~}}{\sum f_{i}}=\frac{90}{15}=6$
Question 14
(IMAGE TO BE ADDED)
So mean $=\frac{\sum f_{i x i}}{\sum f_{i}}=\frac{71}{200}=0.355$
Question 15
Ans: No. of bogs $(n)=25$
Highest score $=25$
Lowest $\operatorname{score}=16$
So Range $=25-16=9$
Now taking class intervals
IMAGE TO BE ADDED)
$\text { mean }=\frac{\sum f x}{\sum f}=\frac{533}{25}=21.32$
So mean mars $=21.32$ marks.
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