Lesson 12.1

Measures of Central Tendency

12.1 Measures of Central Tendency

Objectives: Find the mean, median, and mode of a data set. Find ore estimate the mean from a frequency table of data.

Standards: 2.6.8A. Compare and contrast different plots of data using values of mean, median, mode, and range.

Three commonly used measures of central tendency are the mean, median, and mode.

Ex 1. Using the data 40, 45, 39, 40, 41, 42, 37, 41, 41, 40, find the measures of central tendency (mean, median, and mode),

and compare them.

RANGE = 45 – 37 = 8

mean: 40.6x

TRY THIS: Using the data 88, 74, 98, 76, 68, 74, 89, 92, find the measures of central tendency, and compare

them.

• Mean = 82.375• Median = 82• Mode = 74• Range 98 – 68 = 30

• Mean and Median are very close, where as the mode is lower.

There are 14 people sitting in Hank’s Diner.Their incomes are: $52,000, $48,000, $65,000, $62,000, $38,000, $74,000, $49,000, $41,000, $42,000, $50,000, $64,000, $59,000, $56,000, $70,000

Mean: $55,000 Median: $54,000 Mode: none

Bill Gates walks in… his annual income is $2,642,6002) Find the mean, median, and mode for the incomes of the people in Hank’s Diner.

1) Find the mean, median, and mode for the incomes of the people in Hank’s Diner.

Mean: $227,507 Median: $56,000 Mode: none

Which measure best describes what a typical customer at Hank’s earns per year?

Ex 4. Last month, 6 houses were sold in Souderton. The sale prices were as follows: $140,000, $165,000, $150,000, $300,000, $146,000, and $125,000. Find the mean, median, and mode of the sale prices. Explain which measure best represents the typical sale price of a house in Souderton last month.

Mean = 171, 000

Median = 148, 000

Mode = None

Range = 175,000

Median represents the typical sale price of a house in Souderton.

To make a frequency table, first list each distinct value. Then make a mark for each value in the data set. Finally, count the number of marks to get the respective

frequency for each value, as shown below.

The number of chirps that a cricket makes is related to the temperature. To verify this relationship, a class of 24 students counted cricket chirps for 15 seconds with the following results:

Ex 2. Make a frequency table for the data below on the # of books read by 30 students last month.

Then use your frequency table to find the mean.4, 0, 1, 2, 6, 0, 1, 2, 0, 4, 0, 2, 2, 1, 1,

3, 1, 0, 3, 2, 0, 1, 2, 2, 4, 1, 1, 1, 0, 4 # Books Frequency Product

0

1

2

3

4

5

6

Total

# Books Frequency Product

0 7 0

1 9 9

2 7 14

3 2 6

4 4 16

5 0 0

6 1 6

Total 30 51

1.7x

III. When there are many different values,a grouped frequency table is used. A

grouped frequency table, the values are grouped into

classes that contain a range of values.

*Ex 1. The grouped frequency table at right lists the results of a survey of 80 musicians who were asked how many hours per week they spend practicing.

Estimate the mean # of hours that these musicians practice each week.

Hours Class Mean Frequency Product

1-5 13

6-10 9

11-15 9

16-20 14

21-25 16

26-30 8

31-35 8

36-40 3

Total

Hours Class Mean Frequency Product

1-5 33 13 39

6-10 8 9 72

11-15 13 9 117

16-20 18 14 252

21-25 23 16 368

26-30 28 8 224

31-35 33 8 264

36-40 38 3 114

Total 80 1450

18.125x

*Ex 2. The grouped frequency table lists the numbers of CDs bought by 50 students last year. Estimate the mean # of CDs bought by these students last year.

# CDs Class Mean Frequency Product

0 4

1-5 14

6-10 9

11-15 10

16-20 8

21-25 1

26-30 2

31-35 1

36-40 1Total

# CDs Class Mean Frequency Product

0 0 4 0

1-5 3 14 42

6-10 8 9 72

11-15 13 10 130

16-20 18 8 144

21-25 23 1 23

26-30 28 2 56

31-35 33 1 33

36-40 38 1 38Total 50 538

10.76x