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Use the data in Table 3.2 that relate to month household expenditure (in Rs.) on food of 50 households and

(i) Obtain the range of monthly household expenditure on food.

(ii) Divide the range into appropriate number of class intervals and obtain the frequency distribution of expenditure,

(iii) Find the number of households whose monthly expenditure on food is

(a) less than Rs.2,000

(b) more than Rs.3,000

(c) between Rs.1,500 and Rs.2,500

What are arithmetic-line graphs?

To find the line of best fit, which of the following is minimized?

What is the difference between IFRS and Indian GAAP?

The mean and standard and standard deviation of a group of 100 observations were found to be 20 and 3 respectively. Later on it was found that three observations were incorrect, which were recorded as 21, 21 and 18. Find the mean and standard deviation if the incorrect observations are omitted.

Statement:Should people with educational qualification higher than the optimum requirements be debarred from seeking jobs?

Arguments:

I. No, it will further aggravate the problem of educated unemployment.

II. Yes, it creates complexes among employees and affects the work adversely.

III. No, this goes against the basic rights of the individuals.

IV. Yes, this will increase productivity.

In a village of 200 farms, a study was conducted to find the cropping pattern. Out of the 50 farms surveyed, $50\%$ grew only wheat. Identify the population and the sample here.

There are 60 students in a class. The following is the frequerwy distribution of the marks obtained by the students in a test

$\begin{array}{ccccccc}\text{Marks}& 0& 1& 2& 3& 4& 5\\ \text{Frequency}& x-2& x& x^2& (x+1{)}^2& 2x& x+1\end{array}$

where, x is a positive integer. Determine the mean and standard deviation of the marks.

If the median of the following data is 50, then find p.
$\begin{array}{cccccc}\text{Class}& \text{0-20}& \text{20-40}& \text{40-60}& \text{60-80}& \text{80-100}\\ \text{Frequency}& \text{10}& \text{7}& \text{16}& \text{p}& \text{8}\end{array}$

Calculate $Q_1$ and $Q_3$ from the following data

$\begin{array}{cc}\text{Marks}& \text{Number of}\\ & \text{Students}\\ 10& 4\\ 20& 10\\ 30& 20\\ 40& 8\\ 50& 6\\ 60& 3\end{array}$

Comment whether the following statements are true or false.

(i) The sum of deviation of items from median is zero.

(ii) An average alone is not enough to compare series.

(iii) Arithmetic mean is a positional value.

(iv) Upper quartile is the lowest value of top 25% of items.

(v) Median is unduly affected by extreme observations.

The impact of change in the price of a commodity with little weight in the index will be

(i) small (ii) large (iii) uncertain

State the meaning of frequency curve.

Do samples provide better results than surveys? Give reasons for your answer.

Construct index number of industrial production in the year 2013 from the following data on the basis of 2008’s production:

$\begin{array}{ccccc}\text{Industry}& \text{Unit}& 2008& 2013& \text{Weight}\\ \text{Electrical}\&\text{Electronics}& \text{Mill. Nos.}& 95& 230& 11\\ \text{Transportation}& \text{Mill. Nos}& 302& 667& 14\\ \text{Mechanical}& \text{Mill. Nos.}& 211& 345& 10\\ \text{Sugar and Tea}& \text{Th. Tonnes}& 43& 137& 15\\ \text{Mining}& \text{Th. Tonnes}& 114& 201& 13\\ \text{Textiles}& \text{Mill. Mtrs}& 603& 928& 37\end{array}$

Find unknown frequency in the table given below.

$\begin{array}{cc}\text{X}& \text{Frequency (f)}\\ 5& 5\\ 10& 7\\ 15& ?\\ 20& 10\\ 25& 8\\ 30& 6\\ & \sum f=50\end{array}$

Convert the following 'less than' cumulative frequency series into 'more than' cumulative frequency series:

$\begin{array}{ccccc}\text{Marks less than}& 5& 10& 15& 20\\ \text{Cumulative Frequency}& 12& 25& 35& 55\end{array}$

Which statistical device is used for measuring changes in the magnitude of a group of related variables such as price, the quantity of output, sales, and export?

The distribution of hourly income and the number of employees in a company is given below. Identify the Lorenz curve corresponding to the given distribution.

$\begin{array}{ccccccc}Income& 300& 500& 600& 800& 1200& 1600\\ No.ofemployees& 15& 25& 30& 15& 8& 7\end{array}$

The most accurate mode of data presentation is :

(A) Diagrammatic

(B) Tabulation

(C) Textual method

(D) None of these

Range of the function f(x) = 2x – 3, x Є {3, 5, 7, 9} is:

Find the correlation coefficient using Karl Pearson's formula for the following data.
$\begin{array}{cc}X& Y\\ 10& 2\\ 20& 7\\ 30& 9\\ 40& 11\\ 50& 16\\ 60& 21\end{array}$

Distinguish between quantitative data and qualitative data. Give two examples of each.

State with reason whether the following statements are True or False:

(i) Sum of square of the deviations of items from their arithmetic mean is the maximum.

(ii) Standard Deviation is based on all values.

(iii) For a given set of observations, standard deviation is always more than mean deviation from mean.

Differentiate between economic and non-economic activities.

What is the difference between the upper limit and the lower limit of a class?

Draw a scatter diagram and indicate the nature of correlation.

$\begin{array}{ccccccccc}X& 10& 20& 30& 40& 50& 60& 70& 80\\ Y& 5& 10& 15& 20& 25& 30& 35& 40\end{array}$

Let A = {1, 2, 3, …, 30} and R be the relation “is one-fifth of” on A. Then the range of R is

What are five $I_s$of services?

When is a consumer said to be rational?

An ideal index number would be one which takes into account as weights ______.

Find the first and third quartiles for the following data.

12, 5, 7, 3, 1, 13, 17, 5, 19, 13, 1

Find the equation of the line of best fit for the following data.

$\begin{array}{cc}X& Y\\ 2& 5\\ 5& 7\\ 6& 8\\ 8& 11\\ 10& 12\\ 12& 16\\ 14& 17\end{array}$

Find the median of the following data distribution.

$\begin{array}{ccccccccc}\text{Marks obtained}& 20& 29& 28& 33& 42& 38& 43& 25\\ \text{Number of students}& 6& 28& 24& 15& 2& 4& 1& 20\end{array}$

When resources are limited_____.

The following series relates to the daily income of workers employed in a firm. Compute (a) highest income of lowest 50% workers, (b) minimum income earned by the top 25% workers and (c) maximum income earned by lowest 25% workers.

$\begin{array}{ccccccc}\text{Daily Income (in Rs)}& \text{10 - 14}& 15-19& 20-24& 25-29& 30-34& 35-39\\ \text{Number of Workers}& 5& 10& 15& 20& 10& 5\end{array}$

What is meant by NULL value? What are the reasons that lead to their occurrence in database relations?

The consumer price index for May, 2008 was 110. The food index was 100 and that of other items 150. What is the percentage of the total weight given to food?

Explain four limitations of consumer price index numbers.

If the arithmetic mean of the data given below is 28, find the missing frequency.

$\begin{array}{ccccccc}\text{Profit Per}& 0-10& 10-20& 20-30& 30-40& 40-50& 50-60\\ \text{Retail Shop}& & & & & & \\ \text{Number of}& 12& 18& 27& -& 17& 6\\ \text{Retail Shops}& & & & & & \end{array}$

Check whether the following pair of statements are negations of each other. Give reasons for your answer.

(i) x +y =y +x is true for every real numbers x and y.

(ii) There exists real numbers x and y for which x + y = y + x.

As the price of a packet of peanuts increases by 5 per cent, the quantity supplied of these peanut packets rises by 8 per cent. What is the elasticity of supply for peanut packets ?

Approximately what percentage of the revenue in the year 2011, was the revenue in the year 2009?

Construction of index of industrial production(IIP) in India involves _____.

What is frequency?