Measures of Central Tendency Statistics Measures of Central Tendency

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

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.

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)

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

Find the Mean, Median, and Mode 95 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

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

What’s the mean? Weekly Wages Frequency 130 – 140 11 140 – 150 24 150 – 160 30 160 – 170 10 170 – 180 13 180 – 190 8 190 - 200 4 Why would have trouble finding the mean of this frequency distribution? Can you find the mean without knowing the exact numbers?

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

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 8 190 - 200 4

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

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

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

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?

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