1 Marks Question

Question 11 Mark

Write the formula to find the median for a class frequency distribution.

Answer

$\operatorname{Median}(M)=l+\frac{\frac{N}{2}-C}{f} \times h$

Question 21 Mark

If the standard deviation of a distribution is $15.4$ and the arithmetic mean is $120.2,$ then write its coefficient of variation.

Answer

$\begin{aligned} \text { Coefficient of variation } & =\frac{\sigma}{\bar{x}} \times 100 \\ & =\frac{15.4}{120.2} \times 100 \\ & =12.81 \%\end{aligned}$

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Question 31 Mark

Define mean deviation and write its two properties.

Answer

In any series, the arithmetic mean of the absolute values of the deviations of different values of a variable from its statistical mean (arithmetic mean, median and mode) is called its mean deviation.
Merits : (1) It is based on all the data. If the value of any data changes, then the value of mean deviation also changes.
(2) This measurement is easy to calculate and understand..

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Question 41 Mark

Write the sum of deviations from arithmetic mean in a distribution.

Answer

The sum of deviations is zero.

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Question 51 Mark

Find the range of the following frequency distribution :

Class	10 - 20	20 - 30	30 - 40	40 - 50	50 - 60
Frequency	6	13	10	5	3

Answer

The smallest class is $(10-20)$ and its lower limit $=10$
So, $\quad$ the minimum value $( L )=10$
The upper limit of the largest class $(50-60)$
So, $\quad$ the maximum value $(H)=60$
Hence range $(R)=H-L=60-10=50$

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Question 61 Mark

What do you understand by dispersion? What are its measurements?

Answer

In statistics, the extent to which the numerical data are distributed about an average value is called dispersion or we can say that it is the distribution of data. Dispersion is of two types :
(i) Absolute measure
(ii) Relative measure

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Question 71 Mark

Standard deviation of any distribution is 20.5 and arithmetic mean is 60, then find the coefficient of standard deviation.

Answer

Coefficient of standard deviation
$
\begin{array}{l}
=\frac{\text { Standard deviation }}{\text { Arithmetic mean }} \\
=\frac{20.5}{60}=0.34
\end{array}
$

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Question 81 Mark

Write the formula for the standard deviation.

Answer

Standard deviation $\sigma=\sqrt{\frac{\sum_{i=1}^n x_i^2}{n}-\left(\frac{\sum_{i=1}^n x_i}{n}\right)^2}$

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Question 91 Mark

If price of all the items of a series is same, then find the value of dispersion.

Answer

As the price of all the items is same, dispersion $=0.$

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Question 101 Mark

What is the effect of change of origin on standard deviation?

Answer

There is no effect.

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Question 111 Mark

Is the mean deviation taken from the median smaller or larger than the mean deviation taken from any other value?

Answer

Smaller.

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Question 121 Mark

Write the definition of standard deviation.

Answer

Standard deviation is a statistic that measures the dispersion of a dataset relative to its mean and is calculated as the square root of the variance. The standard deviation is calculated as the square root of variance by determining each data point's deviation relative to the mean.
$\sigma=\sqrt{\sum_{i=1}^n \frac{(x i-\bar{x})^2}{n}}$

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Question 131 Mark

If the variance of a distribution is $16.81,$ then write its standard deviation.

Answer

$\begin{aligned} \text { Standard deviation } & =\sqrt{\text { variance }} \\ & =\sqrt{16.81} \\ & =4.1\end{aligned}$

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