Higher value of co-efficient variation suggests greater degree of variation & lesser degree of stability. Learn interquartile range of deviation MCQs, "Measures of Dispersion" quiz questions and answers for admission and merit scholarships test. According to Prof. C.R. Answer: We have different measures of dispersion used in measuring the variation in a data set. vii) Compare the values of different measures for each crop. Find out central tendency of the series (mean or median) from which deviations are to be taken. Write down the features of mean deviation. \(\overline { X }\) = Mean value. Answer: Answer: NCERT Solution for Class 11 Statistics for chapter 6 Measures of Dispersion. 0000001591 00000 n Answer: Answer: are Rs. Median (M) \(=\frac{N+1}{2}=\frac{10+1}{2}=\frac{11}{2}\) Define quartile deviation. We take the following example for providing that the variance is uneffected by the choice of the assumed mean. What is the difference between Variance and standard deviation? Mean Deviation: Question 8. Define quartile deviation. x = mid value Total wages after increase in wages = 10000 + 1000 + Rs. Range is unduely uneffected by extreme range. Prove by an example that the Variance is uneffected by the choice of the assumed mean. It is not a well – defined measure since mean deviation from different, average (Mean, median & mode) will not be same. In equation, variance = \((\sigma)^{2}\). trailer << /Size 304 /Info 268 0 R /Root 282 0 R /Prev 130891 /ID[<5c38e2c274ce36de66f7fe195cd5b9b7><5c38e2c274ce36de66f7fe195cd5b9b7>] >> startxref 0 %%EOF 282 0 obj << /Pages 278 0 R /Type /Catalog /DefaultGray 279 0 R /DefaultRGB 280 0 R /AcroForm 283 0 R /PageMode /UseThumbs >> endobj 283 0 obj << /Fields [ 188 0 R ] /DR << /Font << /ZaDb 187 0 R /Helv 186 0 R /HeBo 288 0 R >> >> /DA (/Helv 0 Tf 0 g ) >> endobj 302 0 obj << /S 370 /T 491 /V 567 /Filter /FlateDecode /Length 303 0 R >> stream Variance is the square of standard deviation. The amount of Variation in income is shown by deviation from the central values. Deviation from the arithmetic . These short objective type questions with answers are very important for Board exams as well as competitive exams. Total Increase in wages = 50 × 20 = Rs. Range = 100 – 20 = 80, Question 40. Question 33. The following table gives you the height of 100 person. b. compute and apply accurately the descriptive measures in statistics to data analysis and interpretation in solving problems related to research, business, education, technology, science, economics and others. 1. sures of dispersion. Name the measures based on the spread of values Measures of Dispersion Measures of Dispersion - Objective type Online Test Questions and Answers with Solution, Explanation, Solved Problems These measures give us an idea about the amount of dispersion in a set of observations. Other measure can be also dealt with analytically but derivation are harder. Mean deviation 3. When the observations are in kilograms, the absolute measure is also in kilograms. 0000001569 00000 n What is a Lorenz Curve? Symbolically variance = σ². Features of mean deviation. What do you mean by coefficient of variation? Treat all deviations as positive. We can assess how precise is the central tendency observations in the series. 44. H�c```"[V ���ǀ |@6 �(`���f2c}/�ćQ��!g�Ʌ��B? Answer: Calculate range from the following date: It is based on absolute deviation from central values. In the instance where all scores are exactly at the mean, there is no dispersion at all; dis-persion increases from zero as the spread of scores widens about the mean. Dispersion is a measure of the Variation of the items. What is Coefficient of Variation? It is used to compare unifromly, consistency and variability in two different series. Question 9. These solutions for Measures Of Dispersion are extremely popular among Class 11 Commerce students for Economics Measures Of Dispersion Solutions come handy for quickly completing your homework and preparing for exams. Answer: Mean deviation and standard deviation are the measure of dispersion from average. Average of the series refers to the central tendency of the series. \(\mathrm{C.V}_{\mathrm{w}}=\frac{\sigma}{\mathrm{X}} \times 100\) Question 8. C.V = \(\frac{\sigma}{\overline{\mathrm{x}}}\) × 100. 1. a. Answer: What is the main limitation of range? WHEAT Briefly explain the various measures calculated from standard deviation? %PDF-1.2 %���� \(\sigma=\sqrt{\frac{\sum \mathrm{d}^{2}}{\mathrm{n}} \times \mathrm{C}}\). Answer: Mean or Median is used in calculating the mean deviation. Range and quatile deviation measure the dispersion by calculating the spread within which the values lie. = 172 = (-1)2 = 172 – (+1) = 172 – 1 = 171. Question 20. Answer: 1. From the table use come to know that each family have average income of Rs. Question 25. It is calculated by dividing the standard deviation by arithmetic mean of data symbolically. a. demonstrate understanding of the key concepts of the different measures of tendency and measures of variability of a given data. 1. = 1.2 × 10 = 12 In the previous question, calculate the relative measures of variation and indicate the value, which in your opinion is more reliable. Average try to tell only one aspect of a distribution ie. x = deviation Answer: How do Range and Quartile deviation measure the dispersion? Consider the following two sets of data which have the same mean, 25, and the same range, 10, but obvious di erences in the pattern of variability: 2 021 23 4 526 7 8 … The harmonic mean H of the positive real numbers 1, 2, 3, . Based on all values: Not all measures of central tendency and not all measures of disper- 1. Variance = \(\frac{\sum X^{2}}{N}=\frac{5750}{5}\) = 1150 Runs Mean Deviation from A.M. = \(\frac{\sum \mathrm{fd}}{\sum \mathrm{f}}=\frac{998.4}{50}\) = 19.96. Points to remember. Variance \(\frac{\sum x^{2}}{N}=\frac{1710}{10}\) = 171, b. = L – S = 72 – 64 = 8 To check he quality of two breands of light bulbs, their lie in burning hours was estimated as under for 100 bulbs of each brand. 320,400,450,530,550,580,600,610,700.780,800. Since C.V. of bulbs of Brand B (27.34%) is less than that of Brand A (51.55), therefore the bulbs of brand B are more dependable. Question 2. Range and Quantile deviation based on the speread of values. This page contains short questions and answers about Measure of Dispersion which includes introduction to measure of Dispersion or variation, different types of dispersion such as range, standard deviation, variance, … On the other hand, a lower value of coefficient variation suggests lower degree of variability & higher degree of stability, uniformity, homogeneity ‘and consistency. M.D. All questions and answers from the NCERT Book of Class 11 Commerce Economics Chapter 6 are provided here for you for free. Question 38. 2. Question 30. Steps involved in the calculation of mean deviation: Standard deviation is independent of origin as it is not affected by the Value of constant from which deviations are calculated. Only when we study dispersion along with average of series that we can have a comprehensive information about the nature and composition of a statistical series. In calculating standard deviation, algebraic signs are taken into account. Quartile deviation =, Question 5. Absolute measures of dispersion are expressed in terms of original unit of series. 18000. Simple interpretaion: Here Standard deviation = \(\frac{\sigma}{\overline{\mathrm{X}}}\) × 100, 2. Coefficient of variation is a percentage expression of standard deviation. The range is defined as the difference between the largest and the smallest value of variable in the given set of value R = L – S. Question 22. 0000001845 00000 n Median Middle value of rank ordered data Value that separates the higher half of a data set from the lower half Given N-10, Σ X = 10, Σ X2 = 1090 Assumed mean = 45 Quartile deviation 4. representative size of values, to understand it better, we need to know the spread of values also. However, the mean deviation & standard deviation require a little more systematic calculation they, too are easy. Measures of Dispersion 40 Mean Deviation Example The weights of a sample of crates containing books for the bookstore are (in kgs.) Calculation of standard deviation from mean: Question 12. 0000004048 00000 n 0000003813 00000 n Range Quartile deviation, mean deviation and standard deviation arc the important measures of dispersion. Define mean deviation Answer: The arithmetic mean of ‘x’ The range and Quantile deviation do not depend on all values where as the mean deviation and standard deviation use all values of the variable the range is affected the most by extreme values. Answer: The choice is between X and Y on the basis of their five previous scores which are: Which batsman should be selected if we want, Coefficient of S.D. = Rs. 40 = Rs. 1. Calculate the absolute & relative values of dispersion. Σ x = 440, \(\overline{\mathrm{X}}=\frac{440}{10}\) = 44 Answer: Merits: Question 10. It is quite satisfactory when only the middle half of the group is dealt with. Question 2. On the other hand, mean deviation & standard deviation calaculate the variation of value from a central value. Answer: Write down the merits of mean deviation? Co – efficient of variance. 200 Comparison of alternative measure of the dispersion has been discussed below. Each measure has its place in summarizing public health data. The mean deviation of the value ‘x’ about, Question 3. Question 31. Question 32. Coefficient of Variation is the percentage Variation in the mean, the standard being treated as the total Variation in the mean. The units of measurement of the mean deviation are the same as there of the variable. It is very simple & easy measure of dispersion. The range is the easiest one to calculate. Answer: Example: Calculate variance of 25, 60, 45, 30, 70, 42, 36, 48, 34 and 60 by actual mean assumed mean method. They give the answers in the same units as the units of the original observations. Define the range \(\sigma=\sqrt{\frac{\sum x^{2}}{n}-(\bar{x})^{2}}\), Question 17. The measure of central tendencies indicate the central tendency of a frequency distribution in form of an average. Question 10. It involves a harder calculation than the range & quantile deviation. Measures of Dispersion Chapter Exam Instructions. It depends on all the values of the variable. Take from central tendency ignoring signs (+, -) express it as | dx | Or (|dm|). Do you agree? Question 24. Answer: Answer: Question 4. The measurement of the scatter of the given data about the average is said to be a measure of dispersion or scatter. Calculate the range of the following observations : Greater value of dispersion implies lesser representativeness of the central tendency and vice versa. iii) Mean Deviation about mean Answer: Answer: Only mean is used in calculating the standard deviation. Why should we measure dispersion about some particular value? How is coefficient of quartile deviation calculated? The averages represent the series as a whole. , > 0 is defined to be = 1 Example: It ignores 50 percent of the extreme items. iv) Mean Deviation about Median 103, 97, 101, 106, 103. Answer: Question 11. =16, ii) Qusirtile Deviation (Q.D) It is closely Related to standard deviation. Exercise 8.1: Measures of Dispersion. Arithmetic mean. In statistics, the measures of dispersion help to interpret the variability of data i.e. average In this lesson, you will read about the following measures of dispersion : (a) Range (b) Mean deviation from mean (c) Variance 1. 0000014899 00000 n In Equation Variance = (SD)2. Measures of Dispersion •Tell you how widely spread out the values are •Most common are Range, Standard Deviation, and Variance Range •The range of a data set is the difference between the maximum and minimum values in the set •Example: >In {4, 6, 9, 3, 7} the lowest value is 3, and the highest is 9. Question 29. 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