# NCERT Solutions For Class 11 Statistics Chapter 7 Correlation

## Class 11 Statistics Chapter 7 Correlation

NCERT Solutions For Class 11 Statistics Chapter 7 Correlation, (Statistics) exam are Students are taught thru NCERT books in some of state board and CBSE Schools.  As the chapter involves an end, there is an exercise provided to assist students prepare for evaluation.  Students need to clear up those exercises very well because the questions withinside the very last asked from those. S

Sometimes, students get stuck withinside the exercises and are not able to clear up all of the questions.  To assist students solve all of the questions and maintain their studies with out a doubt, we have provided step by step NCERT Solutions for the students for all classes.  These answers will similarly help students in scoring better marks with the assist of properly illustrated solutions as a way to similarly assist the students and answering the questions right.

## Class 11 Statistics Chapter 7 Correlation

Question 1.
The unit of correlation coefficient between height in feet and weight in kgs is
(a) kg/feet
(b) percentage
(c) non-existent
(c) Correlation coefficient (r) has no unit. It is a pure number. It meansss units of measurement are not part of r.

Question 2.
The range of simple correlation coefficient is
(a) 0 to infinity
(b) minus one to plus one
(c) minus infinity to infinity
(b) The value of the correlation coefficient lies between minus one and plus one, -1 ≤ r ≤ 1. If the value of r is outside this range it indicates error in calculation.

Question 3.
If rXY is positive the relation between X and Y is of the type
(a) when Y increases X increases
(b) when Y decreases X increases
(c) when Y increases X does not change
(a) If r is positive the two variables move in the same direction. e.g., when the price of coffee rises, the demand for tea also rises as coffee is a substitute of tea. Therefore, the r between price of coffee and demand for tea will be positive.

Question 4.
If rXY = 0, the variable X and Y are
(a) linearly related
(b) not linearly related
(c) independent
(b) If rXY = 0, it means the two variables are uncorrelated and there is no linear relation between them. However, other types of relation may be there and they may not be independent.

Question 5.
Of the following three measures which can measure any type of relationship?
(a) Karl Pearson’s coefficient of correlation
(b) Spearman’s rank correlation
(c) Scatter diagram
(c) The scatter diagram gives a visual presentation of the relationship and is not confined to linear relations. Karl Pearson’s coefficient of correlation and Spearman’s rank correlation are strictly the measures of linear relationship.

Question 6.
If precisely measured data are available the simple correlation coefficient is
(a) more accurate than rank correlation coefficient
(b) less accurate than rank correlation coefficient
(c) as accurate as the rank correlation coefficient
(a) Rank correlation should be used only when the variables cannot be measured precisely, generally it is not as accurate as the simple correlation coefficient as all the information concerning the data is not utilised in this.

Question 7.
Why is r preferred to covariance as a measure of association?
Both, correlation coefficient and covariance measure the degree of linear relationship between two variables, but correlation coefficient is generally preferred to covariance due to the following reasons

• The correlation coefficient (r) has no unit.
• The correlation coefficient is independent of origin as well as scale.

Question 8.
Can r lie outside the -1 and 1 range depending on the type of data?
No the value of the correlation coefficient lies between minus one and plus one, -1 ≤ r ≤ 1. If the value of r is outside this range in any type of data, it indicates error in calculation.

Question 9.
Does correlation imply causation?
No, correlation measures do not imply causation. Correlation measures co-variation and not causation.
Correlation does not imply cause and effect relation. The knowledge of correlation only gives us an idea of the direction and intensity of change in a variable when the correlated variable changes. The presence of correlation between two variables X and Y simply means that when the value of one variable is found to change in one direction, the value of the other variable is found to change either in the same direction (i.epositive change) or in the opposite direction (i.e., negative change), in a definite way.

Question 10.
When is rank correlation more precise than simple correlation coefficient?
Rank correlation is more precise than simple correlation coefficient in the following situations

• When the Measurements of the Variables are Suspect e.g., in a remote village where measuring rods or weighing scales are not available, height and weight of people cannot be measured precisely but the people can be easily ranked in terms of height and weight.
• When Data is Qualitative It is difficult to quantify qualities such as fairness, honesty etc. Ranking may be a better alternative to quantification of qualities.
• When Data has Extreme Values Sometimes the correlation coefficient between two variables with extreme values may be quite different from the coefficient without the extreme values. Under these circumstances rank correlation provides a better alternative to simple correlation.

Question 11.
Does zero correlation mean independence?
No, zero correlation does not mean independence. If there is zero correlation (rXY = 0), it means the two variables are uncorrelated and there is no linear relation between them. However, other types of relation may be there and they may not be independent.

Question 12.
Can simple correlation coefficient measure any type of relationship?
No, simple correlation coefficient can measure only linear relationship.

Question 13. Collect the price of five vegetables from your local market every day for a week. Calculate their correlation coefficients. Interpret the result.

Question 14. Measure the height of your classmates. Ask them the height of their bench mate. Calculate the correlation coefficient of these two variables. Interpret the result.

Question 15.
List some variables where accurate measurement is difficult.
Accurate measurement is difficult in case of

• Qualitative variables such as beauty, intelligence, honesty, etc.
• It is also difficult to measure subjective variables such as poverty, development, etc which are interpreted differently by different people.

Question 16.
Interpret the values of r as 1, -1 and 0.

• If r = 0 the two variables are uncorrelated. There is no linear relation between them. However, other types of relation may be there and hence the variables may not be independent.
•  If r= 1 the correlation is perfectly positive. The relation between them is exact in the sense that if one increases, the other also increases in the same proportion and if one decreases, the other also decreases in the same proportion.
• If r = -1 the correlation is perfectly negative. The relation between them is exact in the sense that if one increases, the other decreases in the same proportion and if one decreases, the other increases in the same proportion.

Question 17.
Why does rank correlation coefficient differ from Pearsonian correlation coefficient?
Rank correlation coefficient differs from Pearsonian correlation coefficient in the following ways

• Rank correlation coefficient is generally lower or equal to Karl Pearson’s coefficient.
• Rank correlation coefficient is preferred to measure the correlation between qualitative variables as these variables cannot be measured precisely.
• The rank correlation coefficient uses ranks instead of the full set of observations that leads to some loss of information.
• If extreme values are present in the data, then the rank correlation coefficient is more precise and reliable.

Question 18.
Calculate the correlation coefficient between the heights of fathers in inches (X) and their sons (Y).  Note Answer: printed in NCERT is incorrect.

Question 19.
Calculate the correlation coefficient between X and Y and comment on their relationship.   As the value of r is zero, so there is no linear correlation between X and Y.

Question 20.
Calculate the correlation coefficient between X and Y and comment on their relationship. Solution As the correlation coefficient between the two variables is + 1, so the two variables are perfectly positive correlated.

Benefits of NCERT Solution for Class 11

NCERT Solution for Class 11 contains extremely important points, and for each chapter, each concept has been simplified to make it easier to remember and increase your chances of achieving excellent exam results. Exam Preparation References Here are some tips on how these solutions can help you prepare for the exam.

1. This helps students solve many of the problems in each chapter and encourages them to make their concepts more meaningful.
2. NCERT Solution for Class 11 encourage you to update your knowledge and refine your concepts so that you can get good results in the exam.
3. These NCERT Solution For Class 11 are the best exam materials, allowing you to learn more about your week and your strengths. To get good results in the exam, it is important to overcome your weaknesses.
4. Most of the questions in the exam are formulated in a similar way to NCERT textbooks. Therefore, students should review the solutions in each chapter in order to better understand the topic.
5. It is free of cost.

Tips & Strategies for Class 11 Exam Preparation

1. Plan your course and syllabus and make time for revision
2. Please refer to the NCERT solution available on the cbsestudyguru website to clarify your concepts every time you prepare for the exam.
3. Use the cbsestudyguru learning app to start learning to successfully pass the exam. Provide complete teaching materials, including resolved and unresolved tasks.
4. It is important to clear all your doubts before the exam with your teachers or Alex (an Al study Bot).
5. When you read or study a chapter, write down algorithm formulas, theorems, etc., and review them quickly before the exam.
6. Practice an ample number of question papers to make your concepts stronger.
7. Take rest and a proper meal.  Don’t stress too much.

Why opt for cbsestudyguru NCERT Solution for Class 11 ?

• cbsestudyguru provide NCERT Solutions for all subjects at your fingertips.
• These solutions are designed by subject matter experts and provide solutions to every NCERT textbook questions.
• cbsestudyguru especially focuses on making learning interactive, effective and for all classes.
• We provide free NCERT Solutions for class 11 and all other classes.