Median and Its Significance - Dr Richard Diamond

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Median and Its Significance - Dr Richard Diamond

  1. 1. Dr Richard V. Diamond Regent’s College April 2009 The Median. Its Significance
  2. 2. The Median <ul><li>A measure of the central tendency </li></ul><ul><li>What makes a good measure of the central tendency? </li></ul><ul><ul><li>The same amount of data (observations) on each side, left and right </li></ul></ul>Middle value in the ordered array
  3. 3. Locating The Median <ul><li>Median is located by a middle position in data that is arranged from the smallest to largest value </li></ul><ul><li>Where n is number of values (observations) </li></ul><ul><li>If a middle position is a whole number then the median equals to its value. </li></ul><ul><li>If a middle position has a fraction then the median is the average of the two values in the middle </li></ul>Chap 3-
  4. 4. The Median: Resistant to Outliers <ul><li>In the ordered array, the median is the middle number (50% above, 50% below) </li></ul><ul><li>Median is resistant to extreme values (outliers). </li></ul>0 1 2 3 4 5 6 7 8 9 10 Median = 3 0 1 2 3 4 5 6 7 8 9 10 Median = 3
  5. 5. The Mean: Sensitive To Outliers <ul><li>The most common measure of the central tendency </li></ul><ul><li>Affected by extreme values (outliers) </li></ul>Chap 3- 0 1 2 3 4 5 6 7 8 9 10 Mean = 3 0 1 2 3 4 5 6 7 8 9 10 Mean = 4
  6. 6. Measures of Central Tendency: A Comparison Chap 3- House Prices: $2,000,000 $500,000 $300,000 $100,000 $100,000 Sum $ 3,000,000 <ul><li>Mean: ($3,000,000/5) </li></ul><ul><li> = $600,000 </li></ul><ul><li>Median: middle value of ordered data = $300,000 </li></ul><ul><li>Mode: most frequent value = $100,000 </li></ul>
  7. 7. Significance of The Median <ul><li>Even though the mean (average) is the most common measure of the central tendency, the median is used where a statistical measure makes a definitive social impact. </li></ul><ul><ul><li>Median House Price </li></ul></ul><ul><ul><li>Median Income </li></ul></ul><ul><ul><li>Median Age </li></ul></ul>
  8. 8. Age Map of the U.S. Lighter is older median age (white is 46.0 years median age). Dark is younger median age (black is 29.0 years median age) Source: Google Earth
  9. 9. Significance of The Median (Cont.) <ul><li>Median can be used in situations where we cannot get a proper measurement but can only rank data in order </li></ul><ul><ul><li>If we arranged workers in order of their performance, a worker in the middle would literally represent median performance </li></ul></ul><ul><li>We can locate the median by selecting a middle value even if we can’t perform an actual calculation </li></ul>
  10. 10. Locating the Median: A Little Exercise <ul><li>Health care issues are receiving much attention in both academic and political arenas. A sociologist conducted a survey of U.S. citizens over 60 years of age whose net worth is too high to qualify for Medicaid and have no private health insurance. The ages of 25 senior citizens were as follows: </li></ul><ul><li>60, 61, 62, 63, 64, 65, 66, 68, 68, 69, 70, 73, 73 </li></ul><ul><li>74, 75, 76, 76, 81, 81, 82, 86, 87, 89, 90, 92 </li></ul><ul><li>What is the median age of the uninsured senior citizens? </li></ul>

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