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Explanation:

The terms used in calculating standard deviation are deviations from the mean of the observations.
As each number/observation is increased by 2, the deviations from the mean remain the same.
Hence standard deviation remains the same.
On the other hand, median gives the middle term or the average of the two middle terms accordingly when the total number of terms is odd or even.
Thus, it has to increase by 2. 

Hence new median = 20 + 2 = 22 and SD = 4

Concept:

Coefficient of correlation = \(\rm r= \sqrt {b_{xy}\times b_{yx}}\)

Where, b_yx and b_xy are regression coefficients

or the slopes of the equation y on x and x on y are denoted as b_yx and b_xy

Standard deviation = \(\rm \sqrt {Variance }\)

\(\rm \frac{\sigma_y}{\sigma_x}=\frac{b_{yx}}{r}\), \(\rm \sigma_y\) and \(\rm \sigma_x\)are the standard deviation of y and x series respectively.

Calculation:

Here, The two lines of regression are 8x - 10y = 66 and 40x - 18y = 214

⇒ 10y = 8x - 66

⇒ byx = 8/10 = 4/5

And, 

40x - 18y = 214

⇒ 40x =18y + 214

⇒ bxy = 18/40 = 9/20

Now, Coefficient of correlation = \(\rm r= \sqrt {b_{xy}\times b_{yx}}\)

= \(\pm\sqrt {\frac{4}{5}\times\frac{9}{20}}=\pm\sqrt {\frac{9}{25}}=\pm\frac 3 5\)

bxy  > 0 and byx > 0.

So, r = 3/5

Here, variance of x series is 9

⇒ Standard deviation of x series is

 \(\rm \sigma_x\)= √9 = 3

We know, \(\rm \frac{\sigma_y}{\sigma_x}=\frac{b_{yx}}{r}\)

So, \(\rm {\sigma_y}=\frac{b_{yx}}{r}\times ​​\sigma_x\)

\(=\frac{\frac 4 5}{\frac 3 5}\times 3\)

= 4

In Mean deviation, deviations are measured from Mean

A distribution in which the values of mean, median and mode coincide (i.e. mean = median = mode) is known as a symmetrical distribution. Conversely, when values of mean, median and mode are not equal the distribution is known as asymmetrical or skewed distribution. In moderately skewed or asymmetrical distribution a very important relationship exists among these three measures of central tendency. In such distributions the distance between the mean and median is about one-third of the distance between the mean and mode, as will be clear from the diagrams 1 and 2. Karl Pearson expressed this relationship as: 

Mode = mean - 3 [mean - median]

Mode = 3 median - 2 mean

and Median = mode + 2/3 [mean - mode]

H.M is defined as the reciprocal of the mean of the reciprocal of these values  

Standard deviation of a series can have minimum value of  Zero

In S.D signs are ignored 

Factor reversal test & Time reversal test  (c)Both

Factor reversal test  & Time reversal test  (c) Both 

Fisher’s formula satisfies  Unit test

(d) None of these

Index numbers are expressed in  Percentage

Operation condition is not a factor responsible for seasonal variation

Fishers  index number is called Ideal index number.

(c) Both   (Understanding past behavior & Evaluating current program)

 In Laspear’s Index number Base year quantities are used

arithmetic mean  is considered to best average 

Range is an Absolute measure 

 Range = H-L..

In standard deviation, deviations are measured from  Mean

 Squares of S.D is known as variance 

75 values 23 32 85 32 42 10 20 18 28 

(d)None of these

Range is used in quality control 

 Mean deviation is based on all values , so it is more valuable

Time series is a set of values arranged in chronological order 

mode is not a mathematical average 

Median is not capable of algebraic treatment 

 D is Capable of more algebraic treatment 

Cyclic variation Occur at intervals of more than 1 year  

Arithmetic Mean is a mathematical average  

Q.D  is the half distance between the third and first quartiles

(d) All  of these 

arithmetic mean is capable of more algebraic treatment 

Statistical methods are most dangerous tools in the hands of Inexpert

Data are information collected in a systematic manner with the aim of deriving certain related conclusion. Let us discuss the sources for collection of data. 

• The collected data from different sources which are not arranged or organized in any manner are called raw data.
• When data are collected directly from the source i.e., from the students. This is an instance of the data being collected from the primary source.
• The data which are collected indirectly i.e., from the documents containing the information collected for some other purpose. Such indirect sources are called secondary source.
• If the raw data consists of a few scores, then we arrange them in ascending (increasing) or descending (decreasing) order. Then it is called arrayed data. 

Hence, we conclude that the above statement is about raw data.

Concept:

\(\rm Mean\ of\ 'n'\ observations=\dfrac{Sum\ of\ observations}{n}\).

Calculation:

Let's say that the third number is x.

So, Numbers are 4, 12 and x

Here n = 3

As we know, \(\rm Mean\ of\ 'n'\ observations=\dfrac{Sum\ of\ observations}{n}\)

∴ \(\rm 21=\dfrac{4+12+\rm x}{3}\)

⇒ x + 16 = 63

⇒ x = 47.

A distribution is skewed if Mean , Median , Mode are Not equal 

Kurtosis is a measure of peakedness  

Simplest possible measure of dispersion is  Range

When the frequency curve is more peaken than normal curve it is called  Leptokurtic

Measures of dispersion are statistical devices to measure the Variability in a series

Index numbers are devices for measuring differences in the magnitude of a group of related variables 

 (a) Coefficient of variation 

The most important measure of dispersion is Standard deviation

The formula of Q.D is  Q3-Q1/2

Range is the difference between highest and lowest values in a series 

Measures of dispersion are called averages of second order  

 (a) Max O Lorenze.

 If the value of a series are equal , S.D is  Zero