Exercise 8.5 - Chapter 8 Statistics 10th Maths Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

Ex $8.5$
Multiple Choice Questions
Question 1.
Which of the following is not a measure of dispersion?
(1) Range
(2) Standard deviation
(3) Arithmetic mean
(4) Variance
Solution:
(3) Arithmetic mean
Question 2.
The range of the data $8,8,8,8,8 \ldots 8$ is
(1) 0
(2) 1
(3) 8
(4) 3
Answer:
(1) 0
Hint:
Range $=\mathrm{L}-\mathrm{S}=8-8=0$
Question 3.
The sum of all deviations of the data from its mean is
(1) Always positive
(2) always negative
(3) zero
(4) non-zero integer

Solution:
(3) zero
Question 4.
The mean of 100 observations is 40 and their standard deviation is 3 . The sum of squares of all deviations is
(1) 40000
(2) 160900
(3) 160000
(4) 30000
Answer:
(2) 160900
Hint:
$
\begin{aligned}
& \begin{array}{c}
\bar{x}=\frac{\sum x}{n}=40, n=100, \Sigma x=4000 \\
\text { S.D }(\sigma)=\sqrt{\frac{\sum(x-\bar{x})^2}{n}}
\end{array} \\
& 3=\sqrt{\frac{\sum(x-\bar{x})^2}{n}} \text { on Squaring } \\
& \frac{\sum(x-\bar{x})^2}{n}=9 \\
& \Sigma(x-\bar{x})^2=9 \times n=9 \times 100=900 \\
& \Sigma(x-\bar{x})^2=\Sigma\left(x^2-2 x \bar{x}+\bar{x}^2\right)=900 \\
& \Rightarrow \Sigma x^2-2 \bar{x} \Sigma x+\bar{x}^2 \cdot n=900 \\
& \Sigma x 2=900+2 \bar{x} \cdot \Sigma x-\bar{x}^2 \cdot n \\
& =900+2 \times 40 \times 4000-40 \times 40 \times 100 \\
& =3,20,000-1,60,000+900=1,60,900 \\
&
\end{aligned}
$
Question 5.
Variance of the first 20 natural numbers is
(1) $32.25$
(2) $44.25$

(3) $33.25$
(4) 30
Solution:
(3) $33.25$
Question 6.
The standard deviation of a data is 3 . If each value is multiplied by 5 then the new variance is
(1) 3
(2) 15
(3) 5
(4) 225
Answer:
(4) 225
Hint:
Standard deviation $=3$
Each value is multiplied by 5
New standard deviation $=3 \times 5=15$
New variance $=152=225$
Question 7.
If the standard deviation of $\mathrm{x}, \mathrm{y}, \mathrm{z}$ is $\mathrm{p}$ then the standard deviation of $3 \mathrm{x}+5,3 \mathrm{y}+5,3 \mathrm{z}+5$ is
(1) $3 p+5$
(2) $3 \mathrm{p}$
(3) $\mathrm{p}+5$
(4) $9 p+15$
Solution:
(2) $3 \mathrm{p}$
Question 8.
If the mean and coefficient of variation of a data are 4 and $87.5 \%$ then the standard deviation is
(1) $3.5$
(2) 3
(3) $4.5$
(4) $2.5$
Answer:
(1) $3.5$

Hint:
$
\begin{aligned}
\mathrm{CV} & =\frac{\sigma}{\bar{x}} \times 100 \\
87.5 & =\frac{\sigma}{4} \times 100 \\
\sigma & =\frac{87.5 \times 4}{100}=3.5
\end{aligned}
$
Question 9.
Which of the following is incorrect?
(1) $\mathrm{P}(\mathrm{A})>1$
(2) $0 \leq \mathrm{P}(\mathrm{A}) \leq 1$
(3) $\mathrm{P}(\phi)=0(4)$
(4) $P(A)+P(\overline{\mathbf{A}})=1$
Solution:
(1) $\mathrm{P}(\mathrm{A})>1$
Question 10.
The probability a red marble selected at random from a jar containing $p$ red, $q$ blue and $r$ green marbles is
(1) $\frac{q}{p+q+r}$
(2) $\frac{p}{p+q+r}$
(3) $\frac{p+q}{p+q+r}$
(4) $\frac{p+r}{p+q+r}$
Solution:
(2) $\frac{p}{p+q+r}$
Question 11.
A page is selected at random from a book. The probability that the digit at units place of the page number chosen is less than 7 is
(1) $\frac{3}{10}$
(2) $\frac{7}{10}$
(3) $\frac{3}{9}$
(4) $\frac{7}{9}$

Solution:
(2) $\frac{7}{10}$
Question 12.
The probability of getting a job for a person is $\frac{x}{3}$. If the probability of not getting the job is $\frac{2}{3}$ then the value of $\mathrm{x}$ is
(1) 2
(2) 1
(3) 3
(4) $1.5$
Answer:
(2) 1
Hint:
$
\begin{aligned}
& =\mathrm{P}(500)+\mathrm{P}(200)=\frac{15}{50}+\frac{25}{50}=\frac{40}{50}=\frac{4}{5} \\
& \mathrm{P}(\overline{\mathrm{J}})=\frac{2}{3}=1-\frac{x}{3} \\
& \Rightarrow 1-\frac{x}{3}=\frac{2}{3} \\
& \Rightarrow \frac{3-x}{3}=\frac{2}{3} \\
& \Rightarrow 3-x=2 \Rightarrow x=1
\end{aligned}
$
Question 13.
Kamalam went to play a lucky draw contest. 135 tickets of the lucky draw were sold. If the probability of Kamalam winning is $\frac{1}{9}$, then the number of tickets bought by Kamalam is
(1) 5
(2) 10
(3) 15
(4) 20
Solution:
(3) 15
Hint:
$
=\frac{1}{9} \times 135=15
$

Question 14.
If a letter is chosen at random from the English alphabets $\{a, b, \ldots \ldots, z\}$ then the probability that the letter chosen precedes $\mathrm{x}$
(1) $\frac{12}{13}$
(2) $\frac{1}{13}$
(3) $\frac{23}{26}$
(4) $\frac{3}{26}$
Answer:
(3) $\frac{23}{26}$
Hint:
$
=1-\frac{3}{26}=\frac{23}{26}
$
Question 15.
A purse contains 10 notes of $\square 2000,15$ notes of $\square 500$, and 25 notes of $\square 200$. One note is drawn at random. What is the probability that the note is either a $\square 500$ note or $\square 200$ note?
(1) $\frac{1}{5}$
(2) $\frac{3}{10}$
(3) $\frac{2}{3}$
(4) $\frac{4}{5}$
Solution:
(4) $\frac{4}{5}$