Exercise 8.2 - Chapter 8 - Statistics - 10th Maths Guide Samacheer Kalvi Solutions - Tamil Medium

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Ex 8.2
Question 1.
The standard deviation and coefficient of variation of a data are $1.2$ and $25.6$ respectively. Find the value of mean.
Solution:
Co-efficient of variation C.V. $=\mathrm{C} . \mathrm{V}=\frac{\sigma}{\bar{x}} \times 100$
Co-efficient of variation C.V $=\frac{\sigma}{\bar{x}} \times 100$
$
\sigma=6.5, \bar{x}=12.5
$
$
\begin{aligned}
\therefore \quad \text { C.V } & =\frac{6.5}{12.5} \times 100 \% \\
& =52 \% .
\end{aligned}
$
Question 2.
The standard deviation and coefficient of variation of a data are $1.2$ and $25.6$ respectively. Find the value of mean.
Solution:
$
\sigma=1.2, \text { C. V. }=25.6, \bar{x}=\text { ? }
$
$
\begin{aligned}
\mathrm{C} . \mathrm{V}=\frac{\sigma}{\bar{x}} \times 100 \% & \Rightarrow \bar{x}=\frac{\sigma}{\mathrm{C} . \mathrm{V} .} \times 100 \% \\
\bar{x} & =\frac{1.2}{25.6} \times 100 \\
& =4.687=4.69
\end{aligned}
$

Question 3.
If the mean and coefficient of variation of a data are 15 and 48 respectively, then find the value of standard deviation.
Solution:
$
\bar{x}=15, \mathrm{C} . \mathrm{V} .=48, \sigma=\text { ? }
$
$
\begin{aligned}
\mathrm{C} . \mathrm{V} & =\frac{\sigma}{\bar{x}} \times 100 \\
\Rightarrow \quad \sigma & =\frac{\mathrm{C} . \mathrm{V} \cdot \times \bar{x}}{100}=\frac{48 \times 15}{100} \\
& =7.2
\end{aligned}
$
Question 4.
If $\mathrm{n}=5, \bar{x}=6, \Sigma x^2=765$, then calculate the coefficient of variation.
Solution:
$
\begin{aligned}
n=5, \bar{x}=6, \Sigma x^2= & 765, \mathrm{C} . \mathrm{V}=? \\
\sigma & =\sqrt{\left(\frac{\Sigma x^2}{n}\right)-\left(\frac{\Sigma x}{n}\right)^2} \\
& =\sqrt{\frac{765}{5}-6^2} \\
& =\sqrt{153-36} \\
& =10.82 \\
\text { C.V } & =\frac{10.82}{6} \times 100 \% \\
& =180.28 \%
\end{aligned}
$
Question 5.
Find the coefficient of variation of $24,26,33,37,29,31$.
Solution:

$\begin{aligned}
& \bar{x}=\frac{\Sigma x}{n} \\
&=\frac{180}{6} \\
&=30 \\
& \sigma=\sqrt{\frac{\Sigma d^2}{n}} \\
&=\sqrt{\frac{112}{6}} \\
&=\sqrt{18.66} \\
&=4.32 \quad \text { C.V }=\frac{4.32}{30} \times 100 \% \\
& \therefore \text { Co-efficient of variation C.V }=\frac{\sigma}{x} \times 100 \%
\end{aligned}$

Question 6.
The time taken (in minutes) to complete a homework by 8 students in a day are given by 38,40 , $47,44,46,43,49,53$. Find the coefficient of variation.
Solution:
$
\begin{aligned}
\text { Mean } & =\bar{x}=\frac{\Sigma x}{n} \\
& =\frac{38+40+47+44+46+43+49+53}{8} \\
& =\frac{360}{8} \\
& =45 \\
\sigma & =\sqrt{\frac{\Sigma d^2}{n}}=\sqrt{\frac{164}{8}}=\sqrt{20.5} \\
& =4.5
\end{aligned}
$
Co-efficient of variation
C.V. $=\frac{\sigma}{\bar{x}} \times 100=\frac{4.5}{45} \times 100=10.07 \%$
Question 7.
The total marks scored by two students Sathya and Vidhya in 5 subjects are 460 and 480 with standard deviation $4.6$ and $2.4$ respectively. Who is more consistent in performance?
Solution:

Question 8.
The mean and standard deviation of marks obtained by 40 students of a class in three subjects Mathematics, Science and Social Science are given below.

Which of the three subjects shows highest variation and which shows lowest variation in marks?

Solution:

Science subject shows highest variation. Social science shows lowest variation.
Question 9.
The temperature of two cities A and B in a winter season are given below.

Find which city is more consistent in temperature changes?
Solution:

$\therefore$ Co-efficient of variation of City A is less than C.V of City B.
$\therefore$ City $\mathrm{A}$ is more consistent.