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If the covariance between two variables X and Y is 8 and variance of X and Y are respectively 25 and 36, find the correlation coefficient.

Calculate the rank correlation co-efficient between 'X' and 'Y' variables.

$\begin{array}{cccccccc}X& 10& 20& 35& 14& 18& 21& 16\\ Y& 15& 25& 18& 19& 20& 26& 27\end{array}$

Define sample.

A) Distinguish between exclusive method and inclusive method.

B) Why are open-end distributions used?

Calculate the correlation coefficient between the heights of fathers in inches (X) and their sons (Y).

$\begin{array}{ccccccccc}X& 65& 66& 57& 67& 68& 69& 70& 72\\ Y& 67& 56& 65& 68& 72& 72& 69& 71\end{array}$

Name the series in which cumulative frequency can be calculated.

Differentiate between quantitative and qualitative data.

Your local supermarket plays the role of a______.

Mr. Raj, an electronic goods dealer, gifted a microwave of value Rs.30,000 to his friend Rohan and recorded it in books as drawings. Is he correct?

Consumer price index reflects______ inflation.

If the median of the following frequency distribution is 40 and total frequency is 60, then find the missing frequencies.
$\begin{array}{cccccc}Marks& 0-10& 10-30& 30-60& 60-80& 80-90\\ Numberofstudents& 5& f_1& 30& f_2& 2\end{array}$

The importance of Consumer Price index lies in_____.

Find the mean using step-deviation.
$\begin{array}{cc}ClassInterval& Frequency\\ 35-45& 200\\ 45-55& 250\\ 55-65& 50\\ 65-75& 70\\ 75-85& 40\end{array}$ [4 MARKS]

Calculate the coefficient of correlation from the following data:

$\begin{array}{cccccc}X& 30& 40& 60& 70& 100\\ Y& 90& 110& 140& 150& 160\end{array}$

‘The Task Force on Projections of Minimum Needs and Effective Consumption Demand’ was formed in

Give two reasons to use footnotes in a table.

The mean and standard deviation of 20 observation are found to be 10 and 2 respectively. On rechecking, it was found that an observation 8 was incorrect. Calculate the correct mean and standard deviation in each of the following cases :

(i) If wrong item is omitted

(ii) If it is replaced by 12.

Calculate the median from the following data:

$\begin{array}{ccccccccc}\text{Marks (less than)}& 5& 10& 15& 20& 25& 30& 35& 40\\ \text{No. of students}& 4& 10& 20& 30& 55& 77& 95& 100\end{array}$

Briefly explain the purpose of grouping and sorting of the data as a means to refine a report.

Surveys conducted by a Non-Government Organisation reveal that in the state of Punjab, area under pulses has tended to shrink by 40% while the area under rice and wheat has tended to shrink by 20%, between the years 2007-2017. However, other crops like barley and maize have witnessed an increase in area by 43% and 39% respectively over the same period of time.

Why was textual presentation an effective tool for presenting the above data?

What is the relation among the mean, median and mode?

Prepare the frequency array of marks obtained by 25 students of a class in Economics test.

20,15,20,30,40,25,25,30,40,20,35,35,50,15,50,25,40,40,30,50,25,30,30,15,45.

State any two limitations of statistics.

The arithmetic mean of two positive numbers is $2$ more than its geometric mean. If their difference is $8,$ then the numbers are

Calculate mean deviation from mean from the following data using direct method:

2, 4, 7, 8, 9

What is a Lorenz curve?

The following table contains the placement statistics for JKL institute of technology. The first column contains the CGPA or grade of the students and the second column contains the average salary in lakhs per annum. Find the average salary corresponding to 8.5 CGPA using linear interpolation.

$\begin{array}{cc}CGPA\left(X\right)& Salary\left(Y\right)\\ 5& 2.5\\ 6& 4\\ 6.5& 4.5\\ 7& 6\\ 7.5& 7.5\\ 8& 9\\ 9& 11\end{array}$

Ogives can be helpful in locating graphically the

(a) mode (b) mean

(c) median (d) none of these

Shreya was doing an experiment to find out the relationship between voltage (X) and current (Y). The values obtained by Shreya are tabulated below.

$\begin{array}{cc}Voltage\left(X\right)& Current\left(Y\right)\\ 2& 3.5\\ 3& 5.5\\ 4& 8\\ 5& 9.5\\ 6& 12\\ 7& 14.5\\ 8& 16\end{array}$

Find the line of best fit for this data.

Shreya was doing an experiment to find out the relationship between voltage (V) and current (I). The values obtained by Shreya are tabulated below.

$\begin{array}{cc}Voltage\left(V\right)& Current\left(I\right)\\ 2& 3.5\\ 3& 5.5\\ 4& 8\\ 5& 9.5\\ 6& 12\\ 7& 14.5\\ 8& 16\end{array}$

What type of correlation is this?

Find the value of the correlation coefficient from the following table :-

$\begin{array}{ccc}\text{S No}& \text{Age 'X'}& \text{Glucose Level 'Y'}\\ 1& 43& 99\\ 2& 21& 65\\ 3& 25& 79\\ 4& 42& 75\\ 5& 57& 87\\ 6& 59& 81\end{array}$

Calculate coefficient of correlation between age group and rate of mortality from the following data.

$\begin{array}{cccccc}AgeGroup& 0-20& 20-40& 40-60& 60-80& 80-100\\ RateofMortality& 350& 280& 540& 760& 900\end{array}$

Give the formula for finding out median of a continuous series.

Identify the correct statement(s) about the correlation between two variables.

Statement 1: Correlation does not show that there is a causal relationship between two variables
Statement 2: Correlation shows the degree to which variations in one variable explain the variation of the second variable

For an ungrouped data, which of the following is always an observation of the data set?

The ages of five people in a group are 15,25, 30, 35 and 45. From this, a sample of two people having ages 15 and 25 was selected. What is the sampling error of the average age of the group?

Explain any 3 mathematical properties of the coefficient of correlation.

The number of ways in which 10 books can be arranged in a row such that two specified books are side by side is

In town,$25\%$ of the persons earned more than Rs.45,000 whereas $75\%$ earned more than 18,000. Calculate the absolute and relative values of dispersion.

A group or section of the population from whom information is to be obtained is called a ___ .

a) What are the characteristics of a good classification?

b) Explain any 3 merits of tabular presentation.

A measure of dispersion is a good supplement to the central value in understanding a frequency distribution. Comment.

In a class of $5$ students, average weight of the $4$ lightest students is $40$ kgs, average weight of the $4$ heaviest students is $45$ kgs. Then the difference between the maximum and minimum possible average weight is

Calculate the mean and standard deviation for the following table, if the age distribution of a group of people are given below.

$\begin{array}{cccccccc}\text{Age}& 20-30& 30-40& 40-50& 50-60& 60-70& 70-80& 80-90\\ \text{Number of persons}& 3& 51& 122& 141& 130& 51& 2\end{array}$

The number of hours spent studying and percentage marks for 5 students are tabulated below. Find the correlation coefficient using Karl Pearson's formula.

$\begin{array}{cc}\text{No. of hours}& \%\text{Marks}\\ 3& 75\\ 4& 85\\ 5& 80\\ 6& 82\\ 7& 88\end{array}$

Given 4 flags of different colours , how many different signals can be generated, if a signal requires the use of 2 flags one below the other?[By default, repetition is not allowed unless it is said in the question.]

Which of the following scatter charts shows zero correlation?