MEASURES OF CENTRAL TENDENCY

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