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The basic objective of a sample is to draw Inferences about the population from which such sample is drawn. 

Index numbers serves as an economic barometer 

c. index numbers

 Mode = 3 median -2 mean.

When mean = 5, median = 10, mode =  20. 

 The Correct option is d. mean

(a) Wage negotiation and wage contracts

Graphical method of measuring variability is first used by Max.

Measures of dispersion are called averages of second order. 

Lorenz Curve is a geometric method of measuring variability 

Weighted averages are used in the calculation of death rate and birth rate. 

Measures of central tendency are known as averages of first order.

There are three types of frequency distributions - 

(i) Individual Series : In individual series, the frequency of each item or value is only one for example ;marks scored by 10 students of a class are written individually. 

(ii) Discrete Series : A discrete series is that in which the individual values are different from each other by a different amount. 

For example: 

                                  Daily wages           5     10     15     20 

                                  No. of workers       6      9       8        5 

(iii) Continuous Series : When the number of items are placed within the limits of the class, the series obtained by classification of such data is known as continuous serise           

For example:

                       Marks obtained      0-10   10-20     20-30   30-40 

                       No.of students          10       18         22         25 

Difference between Exclusive and Inclusive Series

In chronological classification, the data is classified on the basis of Time

Frequency distribution can also be presented by means of graphs. Such graphs facilitate comparative study of two or more frequency distributions as regards their shape and pattern. The most commonly used graphs are as follows -

(i) Line frequency diagram 

(ii) Histogram 

(iii) Frequency Polygon 

(iv) Frequency curves 

(v) cumulative frequency curves or Ogine curve

Line Frequency Diagram : This diagram is mostly used to depict discrete series on a graph. The values are shown on the X-axis and the frequencies on the Y axis. The lines are drawn vertically on X-axis against the relevant values taking the height equal to respective frequencies.

Histogram : It is generally used for presenting continuous series. Class intervals are shown on X-axis and the frequencies on Y-axis. The data are plotted as a series of rectangles one over the other. The height of rectangle represents the frequency of that group. Each rectangle is joined with the other so as to give a continuous picture.

Histogram is a graphic method of locating mode in continuous series. The rectangle of the highest frequency is treated as the rectangle in which mode lies. The top corner of this rectangle and the adjacent rectangles on both sides are joined diagonally . The point where two lines interact each other a perpendicular line is drawn on OX-axis. The point where the perpendicular line meets OX-axis is the value of mode

Frequency Polygon : Frequency polygon is a graphical presentation of both discrete and continuous series.

For a discrete frequency distribution, frequency polygon is obtained by plotting frequencies on Y-axis against the corresponding size of the variables on X-axis and then joining all the points ;by a straight line.

In continuous series the mid-points of the top of each rectangle of histogram is joined by a straight line. To make the area of the frequency polygon equal to histogram, the line so drawn is stretched to meet the base line (X-axis) on both sides.

Frequency Curve : The curve derived by making smooth frequency polygon is called frequency curve. It is constructed by making smooth the lines of frequency polygon. 

This curve is drawn with a free hand so that its angularity disappears and the area of frequency curve remains equal to that of frequency polygon. 

Cumulative Frequency Curve or Ogine Curve : This curve is a graphic presentation of the cumulative frequency distribution of continuous series. It can be of two types - 

(a) Less than Ogive   and    

(b) More than Ogive.

Less than Ogive : This curve is obtained by plotting less than cumulative frequencies against the upper class limits of the respective classes. The points so obtained are joined by a straight line. It is an increasing curve sloping upward from left to right.

More than Ogive : It is obtained by plotting 'more than‘ cumulative frequencies against the lower class limits of the respective classes. The points so obtained are joined by a straight line to give 'more than ogive‘. It is a decreasing curve which slopes downwards from left to right.

Median and partition values can be known from this curve. The point at which the 'less than‘ and 'more than‘ ogive curves intersect gives the value of median.

The mode of a frequency distribution can be determined graphically by Histogram

The industrial development of a country is reflected by index of industrial production. 

The different types of diagrams can be divided into following heads - 

(1) One dimensional diagrams 

(2) Two dimensional diagrams 

(3) Three dimensional diagrams

(4) Pictograms 

(5) Cartograms 

(1) One Dimensional Diagrams or Bar Diagrams : 

Bar diagrams are the most common types of diagram. A bar is a thick line whose width is shown merely for attention. They are called one dimensional because it is only the length of the bar that matters and not the width. 

Kinds of Bar Diagrams : 

(i) Line Diagrams : When the number of items is large, but the proportion between the maximum and minimum is low, lines may be drawn to economise space. Only individual or time series are represented by these diagrams 

(ii) Simple Bar Diagrams : A simple bar diagram is used to represent only one variable. For example the figures of sales, production etc. of various years may be shown by means of simple bar diagram. The bars are of equal width only the length varies. These diagrams are appropriate in case of individual series, discrete series and time series. 

(iii) Multiple Bar Diagrams : In a multiple bar diagram, two or more sets of interrelated data are represented. Different shades, colors or dots are used to distinguish between the bars. These are used to compare two or more related variables based on time and place. 

(iv) Sub-divided Bar Diagrams : If a bar is divided into more than one parts, it will be called sub-divided bar diagram. Each component occupies a part of the bar proportional to its share in the total. For example total expenditure incurred by a family on various items such as food, clothing, education, house rent etc can be represented by means of sub-divided bar diagram. 

(v) Percentage Sub-Divided Bar Diagrams : Percentage subdivided bars are particularly useful to measure relative changes of data. When such diagrams are prepared, the length of the bar is kept equal to 100 and segments are cut in these bars to represent the components of an aggregate. 

(vi) Profit – Loss Diagrams : If relative change of cost & sales or profit or loss are to be represented with the help of bars, then profit – loss diagram are constructed. These diagrams are similar to percentage sub-divided bars and are prepared in the same way. 

(vii) Duo-Directional Bar Diagrams : In duo-directional bar diagram comparative study of two major parts of data is represented in a single bar. Such duo directional diagrams are represented on both sides of the horizontal axis, i.e. above and below the base line. 

(viii) Paired Bars : If two different informations which are in different units are to be presented then paired bar diagram are used. These bars are not vertical but horizontal and the first scale is in the first half and second scale is in the second half. 

(ix) Deviation Bar Diagram : Deviation bars are popularly used for representing net quantities i.e. net profit, net loss, net exports or net imports etc. Such bars can have both positive or negative values. Positive values are shown above the base line and negative values below it. 

(x) Progress Chart or Gant Chart : These charts are mainly used in factories for comparing the actual production with targeted production. By looking at it, it can be known how much production has been achieved and how much they are lacking behind the capacity. 

(xi) Pyramid Bar Diagram : These diagrams are constructed to show population distribution. The distribution of population according to sex, age, education etc are represented by this diagram. In this diagram, the base line is in the middle and its shape is like a pyramid. 

(xii) Sliding Bar Diagrams : These bars are like deo-directional bars but instead of absolute figures percentages of two variables are shown. One of them is shown on the right side of the base and the other on its left. 

(2) Two Dimensional Diagrams :

In two dimensional diagrams, the height as well as the width of the bars will be considered. The area of the bars represents the magnitude of data. Such diagrams are also known as area diagrams or surface diagrams. The important types are – 

(i) Rectangle diagram 

(ii) Square diagram 

(iii) Circle or Pie diagram 

(i) Rectangle Diagram : Rectangles are often used to represent the relative magnitude of two or more values. The area of rectangles is kept in proportion to the values. They are placed side by side like bars and uniform space is left between different rectangles. The rectangles may be of different types - a) Simple Rectangles 

b) Sub-divided Rectangles

c) Percentage sub-divided Rectangles 

(ii) Square Diagrams : When there is a large difference between the extreme values (example the smallest value is 4 and the biggest value is 800) is such a case square diagram is more appropriate. 

First of all square roots of the given values are calculated and the sides are taken in the proportion of square roots. The squares are drawn on the common base line, serially either in increasing or decreasing heights to have beautiful and attractive appearance. 

For calculating the scale, the area is calculated by squaring its side, on the basis of that value of 1 sq.cm. is calculated. 

(iii) Circle or Pie Diagram : These diagrams are more attractive, therefore, pie diagrams are preferred to square diagrams. These diagrams are used to represent data of population, foreign trade, production etc. 

The square roots of the given values are calculated and then it is divided by some common factor so as to attain the radii for the circles. The area of the circle is calculated by the formula - (π r²) . The sides for squares are taken as the radii for different circles. 

A circle can also be sub-divided on the basis of angles to be calculated for each component. There is 360 degree at the centre of the circle and proportionate sectors are cut taking the whole data equal to 360 degrees. Such a circle is known as sub-divided circle or Angular diagram. 

(3) Three Dimensional Diagrams : 

In three-dimensional diagrams length, width and height (depth) are taken into consideration. If the difference between the minimum and maximum value is so wide as it is difficult to represent them by square or circle diagram, then three dimensional diagram is used. For this cubic roots of the given numbers is calculated. Three dimensional diagrams include cubes, blocks, spheres and cylinders etc. 

(i) Pictorgrams : Pictograms are used by government and nongovernment organizations for the purpose of advertisement and publicity through appropriate pictures. It is a popular technique particularly when statistical facts are to be presented for a layman having no background of mathematics or statistics. For representing data relating to social, business and economic phenomena for general masses in fairs and exhibitions, this method is used. 

(ii) Cartograms : Cartograms or statistical maps are also used to represent data. Cartograms are simple and elementary form of visual presentation and are very easy to understand. While highlighting the regional or geographical comparisons, mapographs or cartograms are generally used.

By deflating of index numbers  We mean adjusting them making allowance for changes in the price levels. 

Classes in which upper limits are excluded from the respective classes and are included in the immediate next class are  Exclusive classes

An index number is a specialized type of Average.

The number of observations in a particular class is called Frequency

If the class mid points in a frequency distribution of age of a group of persons are 25, 32, 39, 46, 53 and 60. The size of class interval is  7.

 If the mid points of the classes are 16, 24, 32, 40, and so on, then the magnitude of the class interval is 8. 

Relative measure of dispersion is also known as coefficient of dispersion. 

1. grammatical errors and misspellings 

2. a copy editor 

3. the story 

4. reader’s.

The distribution which has 2 modes is known as bimodal

 (a) Coefficient of variation

b. standard deviation 

Correct answer is Nirupa Roy

1. dining places

2. town people

3. a shilling

4. Shakespeare

Consumer price index is used for formulation of price policy.

1. Sphinxes’ 

2. King 

3. Sun God 

4. Egyptians

WPI means wholesale price index. 

Fisher’s formula satisfies unit test test

Time series is a set of values arranged in chronological order.  

1. the film 

2. train

3. the young flower girl’s 

4. the English professor.

The base year for index numbers should be normal period. 

 The sum of deviations taken from mean is  0.

Freehand curve  is the easiest of all the methods for measuring trend. 

According to M.M. Blair – “ The simplest to understand, the easiest to make, the most variable and the most widely used type of chart is graph.”.

Graphic presentation is a visual form of presenting statistical data. Graph acts as a tool of analysis and makes complex data simple and intelligible.Graphs are more appropriate in the following cases - 

a) If tendency instead of real measurement is important. 

b) When comparative study of many data series is required on one graph.

c) If estimation and interpolation are to be presented by graph. 

d) If frequency distribution is presented by two or more curves.

 If the shop of the trend line is positive, it shaws rising. 

Consumer price index numbers are prepared for all people.

According to free hand curve method original data are plotted on graph

(i) Should be easy to understand. 

(ii) Clearly and rigidly defined. 

(iii) Based on all the observations. 

(iv) Simple to compute. 

(v) Least affected by fluctuations. 

(vi) Capable of further Algebraic treatment. 

(vii) Sampling stability.

The classification of data according to location is what classification Geographical

The number of parts depends mostly on the nature of the data. However, a table should have the following parts. 

(i) Table No. : Each table should be numbered so that the table may be referred with that number. 

(ii) Title : Every table must be given a suitable title which should be short, clear and complete. 

(iii) Captions : Caption refers to the column heading which explains what the column represents. 

(iv) Stubs : Stubs are the designations of the rows or row headings. (v) Body : It is the heart of the table. The body of the table contains the numerical information. 

(vi) Ruling and Spacing : Ruling and leaving the space depends on the needs of the topic and makes the table attractive and beautiful. 

(vii) Footnotes : In order to explain the figures shown in the table, explanatory notes may be given at the end of the table. 

(viii) Source : At the end of the table, the source or origin of given data is mentioned. 

A pie diagram is also called  Angular diagram