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  1. MEASURES OF CENTRALTENDENCY Measures of central tendency try to describe what we refer to as the center of the data

  2. Here are four sets to look at • A = {2,3,6,7,7,8,9} • B = {2,4,7,7,8,8} • C = {2,7,9} • D = {2,2,2,6,8,9,9,10} Where does the center appear to be for each?

  3. Lets look at them graphically. x x x x x x x 1 2 3 4 5 6 7 8 9 10 A = {2,3,6,7,7,8,9} • x x x x x x • 1 2 3 4 5 6 7 8 9 10 B = {2,4,7,7,8,8} x x x 1 2 3 4 5 6 7 8 9 10 C = {2,7,9}

  4. x x x x x x x 1 2 3 4 5 6 7 8 9 10 A = {2,3,6,7,7,8,9} • x x x x x x • 1 2 3 4 5 6 7 8 9 10 B = {2,4,7,7,8,8} x x x 1 2 3 4 5 6 7 8 9 10C = {2,7,9} x x x x x x x x • 1 2 3 4 5 6 7 8 9 10D = {2,2,2,6,8,9,9,10}

  5. Here are four sets to look at • A = {2,3,6,7,7,8,9} • B = {2,4,7,7,8,8} • C = {2,7,9} • D = {2,2,2,6,8,9,9,10} There are three basic measures of central tendency we will discuss. Mean, Median and Mode

  6. Mode- the most frequent data value • Mode • A = {2,3,6,7,7,8,9} • B = {2,4,7,7,8,8} • C = {2,7,9} • D = {2,2,2,6,8,9,9,10}

  7. Mode- the most frequent data value • Mode • A = {2,3,6,7,7,8,9} 7 • B = {2,4,7,7,8,8} 7 & 8 • C = {2,7,9} ? • D = {2,2,2,6,8,9,9,10} 2 • Weakness to Mode: • May not exist • May not be unique • Unaffected by extreme values • Does not always reflect the center of the data

  8. Mode- the most frequent data value • Mode • A = {2,3,6,7,7,8,9} 7 • B = {2,4,7,7,8,8} 7 & 8 • C = {2,7,9} ? • D = {2,2,2,6,8,9,9,10} 2 • Weakness to Mode: • May not exist • May not be unique • Unaffected by extreme values • Does not always reflect the center of the data • Strength- • The mode provides information about common values or concentration of data. • It can be used with nominal data • Application- Inventory in a shoe store or pizza store

  9. Median- the middle value in a set of data arrange in increasing/ decreasing order. If there is an even number of entries , the median it the average of the two middle values. • Mode Median • A = {2,3,6,7,7,8,9} 7 • B = {2,4,7,7,8,8} 7 & 8 • C = {2,7,9} ? • D = {2,2,2,6,8,9,9,10} 2

  10. Median- the middle value in a set of data arrange in increasing/ decreasing order. If there is an even number of entries , the median it the average of the two middle values. • Mode Median • A = {2,3,6,7,7,8,9} 7 7 • B = {2,4,7,7,8,8} 7 & 8 7 • C = {2,7,9} ? 7 • D = {2,2,2,6,8,9,9,10} 2 7 • Weakness to Median: • It is not always a data value • It does not represent the concentration of data • It is not influenced by the data values Strength- • Unique • It is unaffected by extreme values • Application- prices of homes, salaries of employees

  11. Mean- The mean is the average of all the data values. • Mode Median Mean • A = {2,3,6,7,7,8,9} 7 7 • B = {2,4,7,7,8,8} 7 & 8 7 • C = {2,7,9} ? 7 • D = {2,2,2,6,8,9,9,10} 2 7

  12. Mean- The mean is the average of all the data values. The parameter for mean is µ the statistic is • Mode Median Mean • A = {2,3,6,7,7,8,9} 7 7 6 • B = {2,4,7,7,8,8} 7 & 8 7 6 • C = {2,7,9} ? 7 6 • D = {2,2,2,6,8,9,9,10} 27 6 • Weakness to Mean: • Affected by extreme values • Is not always a data value • Is sometimes confusing Ex: 2.3 kids in a family • Strength- • Most commonly used • Involves all the data values • It is unique • Application- Student test scores

  13. Symbols for Measures of Center Population Statistics Means mu- µ