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Which two of the following statements are true?  a) The sum of the deviations from mean (ignoring algebraic signs) is greater than the sum of the deviations from median (ignoring algebraic signs)  b) Standard deviation is independent of change of origin and change of scale  c) In a symmetrical distribution, mean deviation equals 4/5 of standard deviation  d) In a symmetrical and bell shaped distribution quartile deviation is 1/3 of standard deviation  Choose the correct answer from the options given below

Which two of the following statements are true?  a) The sum of the deviations from mean (ignoring algebraic signs) is greater than the sum of the deviations from median (ignoring algebraic signs)  b) Standard deviation is independent of change of origin and change of scale  c) In a symmetrical distribution, mean deviation equals 4/5 of standard deviation  d) In a symmetrical and bell shaped distribution quartile deviation is 1/3 of standard deviation  Choose the correct answer from the options given below Correct Answer a) and c)

Below are the explanation of the above statements:

1.Deviation:

  •  Method of Mean Deviation does not give accurate results. 
  • The reason is that the mean deviation gives the best results when deviations are taken from the median.
  • But the median is not a satisfactory measure when the degree of variability in a series is very high.
  • And if we compute mean deviation from mean that is also not desirable because the sum of the deviations from the mean (ignoring signs) is greater than the sum of the deviations from the median (ignoring signs).
  • If the mean deviation is computed from a mode that is also not scientific because the value of mode cannot always be determined. Thus, statement A is correct.

2. Standard deviation is independent of the change of origin and but not of scale. Thus, statement B is incorrect.

3. In a symmetrical distribution, the mean deviation equals 4/5 of standard deviation. Thus, statement C is correct.

4 In symmetrical and bell-shaped distribution, quartile deviation is the distance from the median to the lower quartile or to the upper quartile. Thus, statement D is incorrect. 

Related Questions

Which of the following are the correct statements with regard to positive skewed distribution? (A) Mean > Media > Mode (B) Mean < Median < Mode (C) Q3 - Median < Median - Q1 (D) Q3 - Median > Median - Q1 (E) Mean = Median = Mod Choose the correct answer from the options given below:
Which two of the following statements are true?  a) Skewness studies the flatness or peakedness of the distribution  b) A positively skewed distribution curve is stretched more to the right than to the left  c) On the basis of empirical relationship between mean, mode and median for moderately asymmetrical distribution, Karl Pearson's coefficient of skewness can be measured by 3 (Mean -Median) divided by Standard Deviation  d) If mean < mode, the distribution is positively skewed  Choose the correct option from those below: 
Given below are two statements: Statement I: In a classroom assessment, a teacher finds that the distribution of students' score is positively skewed. Hence, the mean of scores will be greater than median and median will be greater than mode. Statement II: When the distribution of students' score is found to be normal, all the three measures of central tendency coincide. In the light of the above statements, choose the most appropriate answer from the options given below:
In the question below are given four statements followed by four conclusions numbered I, II, III and IV. You have to take the given statements to be true even if they seem to be at variance with commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts. Statements: All Stone are Hammer. No Hammer is a Bell. Some Bell are Door. All Door are Window. Conclusions: I. Some Window are Stone. II. Some Window are Bell. III. No window is a stone. IV. Some Bell are Stone.
Consider the following statements: 1) Mean is independent of change in scale and change in origin. 2) Variance is independent of change in scale but not in origin. Which of the above statements is/are correct?
Which of the following statements relating to correlation and reegression are true?
1. The coefficient of correlation is independent of change of origin and scale
2. The coefficient of correlation between the two variables is the arithmetic average of the two regression coefficients
3. The probable error of the coefficient correlation is 0.6745 times of its standard error
4. Coefficient of correlation multiplied by the ratio between the standard deviations of the two variables denotes the slope of the regression line
Select the correct answer:
Consider the following statements:
1. Quartile deviations is more instructive range as it discards the dispersion of extreme items
2. Coefficient of quartile deviaton cannot be used to compare the degree of variations in different distributions
3. There are 10 deciles for a series
Which one of the above statements is/are correct?
Consider the following statements. 1. Mode can be computed from histogram 2. Median is not independent of the change of scale 3. Variance is independent of the change of origin and scale Which of these is/are correct?
Consider the statements given below- A: Relationship between Mean, Median and Mode is : Mode = 3 Median – 2 Mean B: It is also possible that there can be more than one mode or no mode for a data set. C: In a data set, half of the data points are smaller than the median and half of the data points are larger. Which of the above statement(s) is/are TRUE?
Consider the following statements: 1) The sum of deviations from mean is always zero. 2) The sum of absolute deviations is minimum when taken around median. Which of the above statements is/are correct?