Section 3.1 Measures of Central Tendency

(HW: add #4, 5, 6, 36, 42 from text )

EX: Grades 81 68 72 76 94 56 85 80 72 74 63 90

a. Determine the mean grade (round to one more place than the raw data).

b. Randomly select one score and write it down (see p.29 on using calculator to randomize).

c. Take a random sample of four scores and find the sample mean (x)

(see p.29 on using calculator to randomize)

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EX: Arrange the scores above in order, then find the median.

Grades 81 68 72 76 94 56 85 80 72 74 63 90

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EX: 1, 1, 1, 2, 10 Find the mean and median

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EX: 1, 4, 10, 10, 10 Find the mean and median

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Guidelines (continuous data, not discrete) – p. 132

[sketch bell-shaped, skewed right, skewed left and compare mean and median]

Bell-shaped: μ ≈ M

Skewed right: μ > M

Skewed left: μ < M

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EX: (p. 138, #28)

Length of eruption (in seconds) for Old Faithful geyser in Calistoga, California.

108 / 108 / 99 / 105 / 103 / 103 / 94
102 / 99 / 106 / 90 / 104 / 110 / 110
103 / 109 / 109 / 111 / 101 / 101
110 / 102 / 105 / 110 / 106 / 104
104 / 100 / 103 / 102 / 120 / 90
113 / 116 / 95 / 105 / 103 / 101
100 / 101 / 107 / 110 / 92 / 108

Find the mean and median.

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EX: Find the mode for the grades given earlier:

Grades 81 68 72 76 94 56 85 80 72 74 63 90

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bimodal

multimodal

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EX: Two small companies each have ten employees, with the hourly wages

shown. Compare the mean, median and mode for these companies.

Company A: 8, 8, 8, 8, 8, 8, 8, 8, 20, 500

Company B: 8, 8, 8, 8, 20, 20, 500, 500, 500, 500

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Reminder: Mean

Median - ‘middle’

Mode - ‘most’