Central Tendency

What is central tendency? Explain three important measures of central tendency?

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Measures of central tendency are scores that represent the center of the distribution. Three of the most common measures of central tendency are:
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Mean Median Mode

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The Mean
The mean is the arithmetic average of the scores.
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Mean is the average of the scores in a distribution

_ X

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_________ i N

Σ Xi

Mean Example
Exam Scores 75 91 82 78 72 94 68 88 89 75

ΣX =sum all scores n = total number of scores for the sample

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Pros
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Pros and cons of using mean

Summarizes data in a way that is easy to understand. Uses all the data Used in many statistical applications Affected by extreme values 12,000; 12,000; 12,000; 12,000; 12,000; 12,000; 12,000; 12,000; 12,000; 12,000; 20,000; 390,000 Mean = $44,167

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Cons
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E.g., average salary at a company
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Median
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The middle score of the distribution when all the scores have been ranked. If there are an even number of scores, the median is the average of the two middle scores.

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Central Tendency Example: Median
• 52, 76, 100, 136, 186, 196, 205, 150, 257, 264, 264, 280, 282, 283, 303, 313, 317, 317, 325, 373, 384, 384, 400, 402, 417, 422, 472, 480, 643, 693, 732, 749, 750, 791, 891 • The median is the middle value when observations are ordered.
– To find the middle, count in (N+1)/2 scores when observations are ordered lowest to highest.

• Median hotel rate:

– (35+1)/2 = 18 – 317

Median (con’t)
2 2 3 3 4 4 4 4 4 10 Number of Words Recalled in Performance Study

Pros and Cons of Median
• Pros
– Not influenced by extreme scores or skewed distributions. – Good with ordinal data. – Easier to compute than the mean.

• Cons
– May not exist in the data. – Doesn’t take actual values into account.

The mode. The mode is the score with the highest frequency of occurrences. It