Measures of Central Tendency

1
Measures of Central Tendency and Percentiles
(5.7)
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I. Measures of Central Tendency
Mean -
The average
Notation
Median -
The middle number
Notation
Mode -
The number that repeats the most
Notation
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Example
The following scores were given on a test
85, 79, 95, 86, 72, 65, 79, 80, 85, 92, 71, 90
Find the following
mean
82.5
median
Reorder 65, 71, 72, 79, 79, 80, 85, 85, 86, 90,
92, 95
What if there are no numbers that repeat?
mode
What if there are four numbers that repeat three
times each?
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II. Percentiles and Percentile Rank
- Compares individual data to all other data
collected.
Example
What does it mean when a students SAT score of
1040 has a percentile rank of 67?
? 67 percent of all students taking the test (at
that time) tested below a 1040
? The individual student scored better than 67
percent of the other students (taking the test at
that time)
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Recall
Make a box and whisker for the following test
scores
52, 64, 72, 75, 80, 88, 90, 90,
95, 98
lower quartile
upper quartile





72
84
90
52
98
25th percentile
50th percentile
25 of the data falls below this mark
50 of the data falls below this mark
75th percentile
75 of the data falls below this mark
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Example
Vicki sold 30 candy bars for her dance
fundraiser. She wanted to know how she compared
with the others in her club. The data below
represent the number of candy bars sold by all
the members. Find Vickis percentile rank.
20, 14, 12, 38, 30, 18, 20, 45, 48, 30, 27, 25
of sales BELOW 30
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? .5833
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total of sales collected
? The percentile rank is 58
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Open your books to page 231. Look at 11 and 12.