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Mean  is not a patrician value 

According to Free hand curvemethod original data are plotted on graph 

Important use of Index numbers is for  Wage negotiation and wage contracts 

skewness means asymmetry of a distribution  

Index numbers are specialized type of averages 

Index numbers serves as an economic barometer 

A measure of dispersion is an average of  Deviation.

A measure of skewness is only the difference between 2  averages

Skewness may be + or –

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

• The mode is seldom used and its computation is easy, but it is highly unstable and may change with minor shifts in the frequencies from one interval to another. 
• However, there are situations in which the only mode can be used. 
• For example, if a shoe company wants to how which size of shoe it should produce more, it would use mode as a measure of central tendency. The most frequently sold size of the shoes is the mode.
• In the above situation, we can see that '8' is repeated for the highest number of times, so the mode is 8.

Hence, we conclude that in the above situation the mode is 8.

Concept:

Variance: Let x_i for i = 1, 2, 3, …, n be observations then variance is given as:

\(\rm \sigma^2 = \frac{\sum_{i=1}^n (x_i-\bar{x})^2}{n}\)

Properties of variance:

• Var(X + C) = Var(X), where C is a constant.
• Var(CX) = C² × Var(X), where C is a constant.

Calculation:

Given: Var(X) = 5

Each observation is multiplied by 2.

So, new variance = Var(2X)

= 2² × 5

= 20

Concept:

Median: It is the middle value in the given set, while the set is either in increasing or decreasing order.

If the number of observation (n) is odd then median is (n+1)/2th term.

If the number of observation (n) is even then the median is average of nth and (n+1)th term.

Calculation:

Given data are 4.1, 5.2, 6.3, 3.6, 2.4, 6.4, 4.6

Increasing order of given data: 2.4, 3.6, 4.1, 4.6, 5.2, 6.3, 6.4

The number of observation is odd (n = 7)

So, the median is the  (n+1)/2th term or 4th term

Median is 4^th term i.e., 4.6

Concept:

Range: It is the difference between the largest and the smallest number in the set.

Range = Largest number - smallest number

Calculation:

We have 51, 123, 458, 12, 43, 234.

Range = Largest number - smallest number

= 458 - 12

= 446

CONCEPT:

Relationship between Mean, Median and mode:

Mode = 3 Median – 2 Mean

CALCULATION:

Given: In a frequency distribution, the mean and median are 10 and 9 respectively

As we know that, Mode = 3 Median – 2 Mean

⇒ Mode = (3 × 9) - (2 × 10) = 7

Hence, option C is the correct answer.

Concept:

Range: It is the difference between the largest and the smallest number in the set.

Range = Largest number - smallest number

Calculation:

We have 4.1, 25.4, 23.3, 66.5, 21, 70.

Range = Largest number - smallest number

= 70 - 4.1

= 65.9