Measures Of Dispersion1

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Measures Of Dispersion1

  1. 1. Measures of dispersion Chapter 3 First session
  2. 2. Measures of Dispersion (Spread) <ul><li>Measures of central tendency attempt to identify the most representative value in a set of data . In fact, the basic numerical description of a data set requires measures of both center and spread. Some methods of measure of spread include range , quartiles , variance and standard deviation </li></ul>
  3. 3. Various Measures of Central tendency <ul><li>Range </li></ul><ul><li>Quartile Deviation </li></ul><ul><li>Mean Deviation </li></ul><ul><li>Standard Deviation </li></ul><ul><li>These are called absolute measures of dispersion </li></ul><ul><li>Absolute measures have the units in which the data are collected </li></ul>
  4. 4. Relative measure of dispersion is the ratio of a measure of dispersion to an appropriate average from which deviations were measured <ul><li>The important relative measures of dispersion are </li></ul><ul><li>Coefft of Range </li></ul><ul><li>Coefft of Quartile Deviation </li></ul><ul><li>Coefft of Mean Deviation </li></ul><ul><li>Coefft of Standard Deviation </li></ul>
  5. 5. Measures of Variation Variation Variance Standard Deviation Coefficient of Variation Population Variance Sample Variance Population Standard Deviation Sample Standard Deviation Range Interquartile Range Or Interquartile Deviation
  6. 6. Range <ul><li>Measure of Variation </li></ul><ul><li>Difference between the Largest and the Smallest Observations: </li></ul><ul><li>Ignores How Data are Distributed </li></ul>7 8 9 10 11 12 Range = 12 - 7 = 5 7 8 9 10 11 12 Range = 12 - 7 = 5
  7. 7. Formula for Range <ul><li>Range = H - L </li></ul><ul><li>H-Higher vale </li></ul><ul><li>L – Lower Value </li></ul><ul><li> H – L </li></ul><ul><li>Coefficient of of Range = </li></ul><ul><li>H + L </li></ul>
  8. 8. Question no 1 <ul><li>Find the range and coefficient of range from the following values </li></ul><ul><li>25 32 85 32 42 10 20 18 28 </li></ul>
  9. 9. Note <ul><li>For comparison we use coefficient of range </li></ul>
  10. 10. <ul><li>Measure of Variation </li></ul><ul><li>Also Known as Midspread </li></ul><ul><ul><li>Spread in the middle 50% </li></ul></ul><ul><li>Difference between the First and Third Quartiles </li></ul>Interquartile Deviation Data in Ordered Array: 11 12 13 16 16 17 17 18 21 <ul><ul><li>Not Affected by Extreme Values </li></ul></ul>
  11. 11. Interquartile range <ul><li>The interquartile range is another range used as a measure of the spread. The difference between upper and lower quartiles (Q 3 –Q 1 ), which is called the interquartile range, also indicates the dispersion of a data set. The interquartile range spans 50% of a data set, and eliminates the influence of outliers because, in effect, the highest and lowest quarters are removed. </li></ul><ul><li>Interquartile range = </li></ul><ul><li>Difference between upper quartile (Q 3 ) and lower quartile (Q 1 ) </li></ul>
  12. 12. Disadvantage <ul><li>It does not measure the spread of the majority of values in a data set—it only measures the spread between highest and lowest values. As a result, other measures are required in order to give a better picture of the data spread </li></ul>
  13. 13. Semi-quartile range OR Quartile Deviation <ul><li>The semi-quartile range is another measure of spread. It is calculated as one half the difference between the 75 th percentile (often called Q 3 ) and the 25 th percentile (Q 1 ). The formula for semi-quartile range is: </li></ul><ul><li>(Q 3 – Q 1 ) ÷ 2 </li></ul><ul><li>. Since half the values in a distribution lie between Q 3 and Q 1 , the semi-quartile range is one-half the distance needed to cover half the values </li></ul>
  14. 14. Semi-quartile range   <ul><li>The semi-quartile range is hardly affected by higher values, so it is a good measure of spread to use for skewed distributions, but it is rarely used for data sets that have normal distributions. In the case of a data set with a normal distribution, the standard deviation is used instead. </li></ul>
  15. 15. Question no <ul><li>Compute the inter quartile range and quartile deviation for the following series. </li></ul><ul><li>23 25 8 10 9 29 45 85 10 16 </li></ul><ul><li>QD=11.625 </li></ul><ul><li>Inter quartile range=23.25 </li></ul>
  16. 16. Coefficient of Quartile deviation <ul><li>Q3-Q1 </li></ul><ul><li>Coefficient of Quartile deviation= </li></ul><ul><li>Q3+Q1 </li></ul>
  17. 17. Question <ul><li>Find the quartile deviation and coeffient of quartile deviation from the following data </li></ul><ul><li>22 26 14 30 18 11 35 41 12 32 </li></ul>
  18. 18. Question <ul><li>Find the median ,quartile deviation and coeffient of quartile deviation from the following data </li></ul><ul><li>Obtained 0-10 10-20 20-30 30-40 40-50 50-60 </li></ul><ul><li>No of 12 18 27 20 17 6 </li></ul><ul><li>Students </li></ul>

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