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STATISTICS Measures of Center
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STATISTICS Measures of Center. Mean…… The mean is the average of a set of numbers.

Dec 28, 2015

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Page 1: STATISTICS Measures of Center. Mean…… The mean is the average of a set of numbers.

STATISTICSMeasures of Center

Page 2: STATISTICS Measures of Center. Mean…… The mean is the average of a set of numbers.

Mean……• The mean is the average of a set of numbers.

valuesofnumbertotal

numberstheofsummean

)(

Page 3: STATISTICS Measures of Center. Mean…… The mean is the average of a set of numbers.

Example……

• Roy compared the prices of a cd player at 5 stores. The prices at each store were $80, $95, $60, $90, and $85.

• What was the mean price of the cd players?

• Answer:

825

4105

)8590609580(

mean

mean

Page 4: STATISTICS Measures of Center. Mean…… The mean is the average of a set of numbers.

Example……

• George’s scores on 3 math tests were 70, 80, and 86.

• What score does he need to make on the 4th test to have a final average of 84?

• Answer:

100

236336

236)4)(84(4

)236(84

4

)868070(84

x

x

x

x

x

Page 5: STATISTICS Measures of Center. Mean…… The mean is the average of a set of numbers.

Median……• Definition: The number in the center of the data.

a. Odd # in set – median is middle number.

b. Even # in set – median is the

average of the 2 numbers in the center.

c. The numbers must be in order from smallest to largest.

Page 6: STATISTICS Measures of Center. Mean…… The mean is the average of a set of numbers.

Example……

• Consider the following scores:

• 95, 30, 100, 100, and 95.

• Find the median.

• Arrange in Order:

30, 95, 95, 100, 100

• Odd # in set – median is the middle number.

30, 95, 95, 100 100

Page 7: STATISTICS Measures of Center. Mean…… The mean is the average of a set of numbers.

Example……

• Use the following numbers:

• 8, 9, 9, 10, 11, 11

• Find the median.

• Even # in set:• Average the 2 middle numbers:

8, 9, 9, 10, 11, 11

5.92

19

2

)109(

median

median

Page 8: STATISTICS Measures of Center. Mean…… The mean is the average of a set of numbers.

Example……

• Tracey had scores of 11, 10, 12, 6, 6, and 8 on her math quizzes. What is her median score?

• Arrange in Order 1st:

6, 6, 8, 10, 11, 12• Even # in set – average the 2 in the middle.

6, 6, 8, 10, 11, 12

92

18

2

)108(

median

median

Page 9: STATISTICS Measures of Center. Mean…… The mean is the average of a set of numbers.

Mode……• The number that appears the most often.

• There can be more than one mode.

• There can also be no mode if each item appears only once.

Page 10: STATISTICS Measures of Center. Mean…… The mean is the average of a set of numbers.

Example……

• Tony had scores of 12, 11, 10, 9, 10, 11, 12, 10, 11, 11.

• What is the mode of his scores?

• Answer:• It helps to put them in order to see the grouping:

9, 10,10,10, 11,11,11,11,12,12

• The mode is 11.

Page 11: STATISTICS Measures of Center. Mean…… The mean is the average of a set of numbers.

Example……

• Tina had scores of 90, 96, 94, 90, 98, and 94 on her science tests.

• What is the mode?

• Put in order first:

90, 90, 94, 94, 96, 98

• 2 scores appear twice (the most).

• The mode is 90 and 94.

Page 12: STATISTICS Measures of Center. Mean…… The mean is the average of a set of numbers.

Example……

• Find the mode for the high temperatures for the week.

• 97, 92, 88, 99, 90, 91, and 94.

• Put in order first:

88, 90, 91, 92, 94, 97, 99

• Each number occurs only once, therefore there is no mode.

Page 13: STATISTICS Measures of Center. Mean…… The mean is the average of a set of numbers.

Range……• Definition:

The range is the difference between the greatest and least values of the data set.

Page 14: STATISTICS Measures of Center. Mean…… The mean is the average of a set of numbers.

Example……

• Joyce’s bowling scores are 148, 195, 193, 145, 186, and 149.

• What is the range of her scores?

• Find the highest number and the lowest number in the set.

148, 195, 193, 145, 186, 149

• Subtract 195 and 145.

50145195 range

Page 15: STATISTICS Measures of Center. Mean…… The mean is the average of a set of numbers.

Which is the best to use?• Mean, median, and mode are called measures of central

tendency. They tell something about where the data tends to cluster, or where the center of the data is located.

• When the range is small, the mean is most likely to be the best measure of central tendency.

Page 16: STATISTICS Measures of Center. Mean…… The mean is the average of a set of numbers.

Example……• Ted’s earnings for 5 weeks were $84, $76, $86, $300, and

$76.

• Which measure of central tendency best describes her typical wage?

• Why?

Page 17: STATISTICS Measures of Center. Mean…… The mean is the average of a set of numbers.

$76, $76, $84, $86, $300• Mode = 76. It is too low because it is less than 3 other

measures. NO• Mean = 124.4. It is too high because it is greater than 4

of the 5 salaries. NO• Range = 224. Very Big. Mean is probably not good to

use. • Median = 84. It is the most representative of the data.

YES.

Page 18: STATISTICS Measures of Center. Mean…… The mean is the average of a set of numbers.

BOX PLOTS(BOX AND WHISKERS)

Page 19: STATISTICS Measures of Center. Mean…… The mean is the average of a set of numbers.

Boxplot• A graph of a set of data obtained by drawing a horizontal

line from the minimum to maximum values with quartiles labeled in between.

• It is a graphical plot of 5 specific values called the 5-number summary.

Page 20: STATISTICS Measures of Center. Mean…… The mean is the average of a set of numbers.

5-number summary…..Minimum – lowest number in set

Q1- middle number of the lower half

Median – middle number of entire set

Q3 – middle number of upper half

Maximum – highest number in set

Page 21: STATISTICS Measures of Center. Mean…… The mean is the average of a set of numbers.

Steps……• 1. Find the 5-number summary.

• 2. Draw and label a scale of equal intervals.

• 3. Place dots above the 5 numbers

• 4. Put a box around Q1 and Q3.

• 5. Draw a vertical line through the median.

• 6. Draw “whiskers” from the minimum to Q1 and maximum to Q3.

Page 22: STATISTICS Measures of Center. Mean…… The mean is the average of a set of numbers.

Example……• Draw a box plot of the following data.

33, 38, 43, 30, 29, 40, 51, 27, 42, 23, 31

Page 23: STATISTICS Measures of Center. Mean…… The mean is the average of a set of numbers.

Example……• Draw a box plot of the following data.

59, 60, 65, 52, 51, 64, 71, 48, 47, 40, 50

Page 24: STATISTICS Measures of Center. Mean…… The mean is the average of a set of numbers.

Assignment……• Worksheet.