1. Measures of Central Tendency
Statistics
Measures of Central Tendency

2. Essential Question
What are the different ways to measure the central tendency of a data set?

3. Warm UP # 2
The gram of fat in various sandwhiches served by national fast-food restaurants are listed below:
18, 27, 15, 23, 27, 14, 15, 19, 39, 53, 31, 29, 12, 43, 38, 4, 10, 9, 21, 31, 31, 25, 28, 20, 22, 46, 15, 31, 16,20, 30, 8, 18, 15, 7, 9, 5, 8
What is the range of the data?
Determine the appropriate class interval.
What are the class marks?
Construct a frequency distribution of the data.
Draw a histogram.
Name the interval/s that describe the fat content of most sandwiches.

4. What one number best describes this data set?
Salary (Thousands of dollars)
Frequency
20 – 26 6
26 – 32 30
32 – 38 38
38 – 44 33
44 – 50 13
What statistical terms do we use to describe data so that one number represents the data?
Mean (Average)
Median (Middle)
Mode (Most Frequent)

5. Mean – Median - Mode Arithmetic Mean ( )
Median – Middle Value, odd set – exact middle, even set – average of the two middle values
Mode – most frequent
Bimodal – 2 that tie for most frequent
A data set can have no mode if there are 3 or more that are most frequent

6. Find the Mean, Median, and Mode95 52 72 85 89 78 65 77 70 82 75 96 35 88 92 81 30 55 76 83 61 68 73 99 74 54 91 67 71 80

7. Find the Mean, Median and Mode
Which measure of central tendency seem most representative of the set of data?
Explain
Are we OK with mean, median and mode?
Are there outliers?
What happen if to the data if the outlier/s are removed?
Country
Number of Immigrants
China
41,700
Cuba
26,500
Dominican Republic
39,600
India
44,900
Jamaica
19,100
Mexico
163,600
Philippines
55,900
Russia
19,700

8. What’s the mean? Weekly Wages Frequency 130 – 140 11 140 – 150 24
150 – 160 30
160 – 170 10
170 – 180 13
180 – 190 8 4
Why would have trouble finding the mean of this frequency distribution?
Can you find the mean without knowing the exact numbers?

9. Mean of a Frequency Distribution
f – represents the frequency
xi – represents the class mark
k – represents the number of classes

10. Now lets try finding the mean
Weekly Wages
Frequency xi
fi·xi
130 – 140 11
140 – 150 24
150 – 160 30
160 – 170 10
170 – 180 13
180 – 190 8 4

11. Now you try finding the mean
Salary (Thousands of dollars)
Frequency xi
fi·xi
20 – 26 6 23
138
26 – 32 30 29
870
32 – 38 38 35
1330
38 – 44 33 41
1353
44 – 50 13 47
611
120
4302

12. Find the median class:
Take the cumulative frequency divide by 2

13. Season
New Plays
1960 48
1973 43
1986 41
1961 53
1974 54
1987 32
1962
1975 55
1988 30
1963 63
1976
1989 35
1964 67
1977 42
1990 28
1965 68
1978 50
1991 37
1966 69
1979 61
1992 33
1967 74
1980 60
1993
1968
1981
1994 29
1969 62
1982
1995 38
1970 49
1983 36
1996
1971
1984
1997
1972
1985
1998 20

14. From the Previous Data do the following:
Make a stem-and-leaf plot of the number of new productions for the seasons listed
Find the mean of the data
Find the median of the data
Find the mode of the data
What is a good representative number for the average of the new Broadway productions for the seasons 1960 – 1998?

15. Revisiting the EQ:
What are the different ways to measure the central tendency of a data set?