Measures of Central Tendency

Measures of Central Tendency

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Measures of Central Tendency Overview

• Mean:  average for a set of data.

• Median:  The middle value for a data set listed in order.

• Mode:  The most frequently occurring value(s) in a set of data.

• Range:  The difference between the highest and lowest values in a set of data.

• Outlier:  The value(s) that is very different from the rest of the data in a set.  (Affects the Mean)

Finding our measures of central tendency

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Multiple Choice

Find the median, mode and range:

3, 5, 7, 9, 11, 8, 3

• median:7 mode:3 range:10

• median:6 mode:3 range:7

• median:7 mode:3 range:8

Multiple Choice

In which dataset is the median value equal to the mean value?

• {2, 4, 6, 7, 8}

• {12, 18, 20, 23, 24}

• {16, 17, 18, 19, 20}

• {50, 60, 65, 75, 85}

Suppose you scored an 83%, 74%, 95% and 76% on your last four math tests.  If you want to earn an 85% in the class, what must you get on your next math test?

Multiple Choice

Paulo got these markers in three tests: 72, 80 and 82. He had one more test to sit. He wanted an average of 80 for the four tests. What mark must he get in the fourth test?

• 78

• 80

• 84

• 86

Multiple Choice

The heights of six students in a class are given below:

158cm 172cm 164cm

164cm 167cm 159cm

However, there were actually seven students in the class, and the mean height in the class was 165 cm. What was the height of the unknown student?

• 164 cm

• 166 cm

• 171 cm

• 169 cm

Multiple Choice

The heights of the starting 5 players on a basketball team are 60 inches, 67 inches, 64 inches, and 65 inches.  If the mean or balance point of the players is 65, what is the height of the 5th player?

• 70
• 69
• 61
• 68

Open Ended

Suppose you scored a 99%, 67%, 83% and 86% on your last four science tests. If your next test counts twice, is it possible to average a 90%? Explain your answer.

Open Ended

You and your friend have a friendly competition going on about the scores on your math quizzes. Both of your scores for the first five quizzes are given below. Find the mean, median and mode of both sets of data.

Your scores: 18, 16, 19, 15, 17 Mean: ____ Med: ____ Mode: _____

Friend’s scores: 20, 20, 13, 12, 17 Mean: ____ Med: ____ Mode: ____

Do you or your friend have the higher mean? __________

Who has the highest median? __________

Boxplots

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Multiple Choice

What was the lowest score?

• 20

• 30

• 39

• 40

Multiple Choice

What was the median score?

• 39

• 50

• 55

• 16

Multiple Choice

What is the lower quartile?

• 39

• 40

• 35

• 50

Multiple Choice

What is the upper quartile?

• 39

• 50

• 55

• 68