Download Statistics Day 4 Mean, Median, Mode.notebook

Statistics Day 4 Mean, Median, Mode.notebook
Do Now
1) Determine whether each data set is qualitative or quantitative.
a. favorite movies b. number of classmates who are taking Spanish
2) You want to determine what percent of teens ages 14 to 18 watch wrestling on TV.
You go to a high school wrestling match and ask every third teenager whether he or she watches
wrestling on TV. Explain how this might cause bias in the results of your survey.
Mar 11­1:07 PM
Aim: To find the mean, median, and mode of a set of data.
April 11, 2013
Date:
Measures of Central
Tendency:
Mean,Median,
and Mode
Objective: Compare and contrast the appropriateness of different measures of central tendency for a given data set. (AS4)
Mar 22­9:53 AM
Example
1) Find the mean of 93, 80, 86, 72, and 94.
The Mean
The mean is the numerical average.
To find the mean of a set of N numbers, add the numbers and divide the sum by N.
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Apr 1­5:38 AM
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Statistics Day 4 Mean, Median, Mode.notebook
The Median
The median is the number in the middle of the ordered data.
First arrange the numbers in numerical order.
a) The median is the middle number.
b) If there are two numbers in the middle, the median is the average (mean) of those two numbers.
Jan 2­2:45 PM
The Mode
The mode is the number that appears the most in a set of data.
• If one number appears most often in the data, that number is the mode. (one mode)
• If two or more numbers appear more often than all other data values, and these numbers appear with the same frequency, then each of these numbers is a mode. (more than one)
April 11, 2013
Examples: Find the median.
2) 4, 7, 9, 12, 14, 20
3) 5, 6, 9, 10, 14
4) 5, 2, 8, 10, 3, 5, 8, 9
Apr 1­5:40 AM
Examples: Find the mode.
5) 3, 5, 5, 5, 7, 8, 10
6) 2, 2, 4, 6, 6, 8, 9, 10, 10
7) 2, 2, 5, 5, 6, 6, 8, 8
• If each number in the set of data appears with the same frequency, there is no mode.
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Apr 1­5:45 AM
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Statistics Day 4 Mean, Median, Mode.notebook
Outlier is a score out of range from the
other data.
How does an outlier affect the mean,
median, and mode?
Normal listing of scores
65, 70, 75, 76, 77, 80, 82, 84,
86, 89, 90, 92, 93, 95, 97
mean: 83.4
median: 84
mode: none
Apr 1­5:48 AM
8) Determine the modal interval then determine which interval contains the median.
Frequency
Interval
(commuting distance) (number of workers)
50 ­ 59
40 ­ 49
30 ­ 39
20 ­ 29
10 ­ 19
0 ­ 9
1
0
9
4
15
21
N = 50
Apr 1­5:52 AM
April 11, 2013
Data with an outlier
0, 65, 70, 75, 76, 77, 80, 82,
84, 86, 89, 90, 92, 93, 95, 97
mean: 79
median: 83
mode: none
Mean is affected by an outlier. The median
may be slightly affected by it, but the mode
is not affected.
Without the outlier:
median: 84
mean: 83.4
mode: none
Apr 1­5:48 AM
Summary:
Mean ‐ Average of data
Median ‐ Middle number (odd # of data) OR Average of two middle numbers (even # of data)
(DATA IN ORDER 1ST)
Mode ‐ Data that occurs most often Could have one mode, more than one mode, or no mode.
Oct 28­8:10 PM
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Statistics Day 4 Mean, Median, Mode.notebook
PRACTICE:
1) Sid received grades of 92, 84, and 70 on three tests. Find his average.
2) Sarah’s grades were 80 on two tests, and 90 on each of three tests. Find her average.
Apr 1­5:56 AM
5) A set of data consists of six numbers: 7, 8, 8, 9, 9, and x. Find the mode of the six numbers when:
a. x = 9
April 11, 2013
3) What is the median age of a family whose members are 42, 38, 14, 13, 10, and 8 years old?
4) The test scores for an exam were 62, 67, 67, 70, 90, 93, and 98. What is the median score?
Apr 1­5:59 AM
6) Which statement is true for the set of data
5, 5, 6, 7, 7.
a. mean = mode
b. mean = median
c. median = mode
b. x = 8
d. mean < median
c. x = 7
Apr 1­6:06 AM
Apr 1­6:04 AM
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Statistics Day 4 Mean, Median, Mode.notebook
7) Which statement is true for the set of data 8, 8, 9, 10, 15.
a. mean < median
April 11, 2013
8) For which set of data is there no mode?
a. 2, 1, 3, 1, 2
b. 1, 2, 4, 3, 5
b. median < mode
c. 1, 2, 3, 3, 3
c. mean > mode
d. 2, 2, 3, 3, 3
d. mean = median
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9) For which set of data does the median equal the mode?
Apr 1­6:11 AM
10) John received scores of 90, 79, 95, and x. What score must he receive on the 4th test to have a 90 average?
a. 3, 3, 4, 5, 6
b. 3, 3, 4, c. 3, 3, 4, 5
d. 3, 4
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Statistics Day 4 Mean, Median, Mode.notebook
April 11, 2013
11) The scores 12, 15, 17, and x have a mean of 18. What is the value of x?
HOMEWORK:
p.687­689 #3­15 odd, 23­33 odd
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Apr 1­6:20 AM
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