LESSON 30 - Central Tendency

8/7/2019 LESSON 30 - Central Tendency

1/15

Amount Spent Number

$0-$2.99 8

$3.00-$5.99 10

$6.00-$8.99 5

$9.00-$11.99 2

Carolsurveysherclassmatesfortheamountofmoneytheyspent

overtheweekend.Thetablebelowshowsthisdata.

DO NOW!

Basedonthedata,whichtypeofgraph

isbesttodisplayCarolsdata?Explain.


2/15

LESSON 30: Central Tendency7.S.4 and 7.S.5


3/15

What is meant by CENTRAL TENDENCY?

Measures of central tendency describe the middle or averageof a set of data. They are ways of identifying one number thatis a good representation of a group of numbers.

What are the different measures of central tendency?

MEAN MEDIAN MODE


4/15

MEAN = The mathematical middle

Find the sum of the data in the set and divide by the numberof items in the set.

EXAMPLE Data: 65, 70, 72, 74, 90

Step 1: Add the numbers.

65 + 70 + 72 + 74 + 90 = 371

Step 2:Divide the sum by the number of

items in the set.

371 5 = 74.2


5/15

Set #116, 20, 18, 14, 17 17

Set #2

17, 31, 29, 42, 17, 36, 24 28

Find the mean of the following two sets of data:


6/15

MEDIAN = The middle number in a data setPlace the numbers in order, from least to greatest andchoose the middle value.

Data: 65, 70, 72, 74, 90

65, 70, 72, 74, 90

What about for this data set?

65, 70, 71, 72, 74, 90

If there are two middle numbers the median is middle

of those 2 numbers.

65, 70, 71, 72, 74, 90

71 + 72 2 = 143 2 = 71.5


7/15

Set #1

16, 20, 18, 14, 17 17Set #2

17, 31, 29, 42, 17, 36, 24 29

Set #3

11, 7, 9, 6, 14, 19, 15, 13, 5, 3, 8, 10

Find the median of the following sets of data:


8/15

MODE = The number that occurs the most

When there is only one of each number,

there is no mode.

For example: 65, 70, 71, 72, 74, 90

Data: 65, 65, 70, 71, 72, 74, 90

65, 65, 70, 71, 72, 74, 90

65 is the mode

There can be two modes.For example: 65, 65, 70, 72, 74, 74, 90This data set is bimodal.

If there are more than 2modes,

there is NO MODE


9/15

Find the mode of the following two sets of data:

Set #1

16, 20, 18, 14, 17, 18

18

Set #2

17, 31, 29, 42, 31, 17, 36, 24

17

Set #3

13, 18, 13, 19, 32, 24, 18, 15, 16, 33, 24

NO MODE


10/15

Range =

The smallest number subtracted from the largest

Example: 8, 10, 6, 9, 8, 7

Largest = 10

Smallest = 6

10 - 6 = 4

Range = 4

Set #1

16, 20, 18, 14, 17 6

Set #2

17, 31, 29, 42, 17, 36, 24 25

Find the range of the following two sets of data:


11/15

PRACTICE: Find the mean, median, modeand range of these sets of data.

Mean = 40 Mode = 20, 40Median = 35 Range = 80

Set #1:

20, 30, 40, 10,

20, 90, 70, 40

Set #2:157, 124, 142,

119, 100, 101, 97

Mean = 120 Mode = No mode

Median = 119 Range = 60


12/15


13/15

Exam scores for a small advanced math class are provided below.

87, 99, 75, 87, 94, 75, 35, 88, 87, 93

Find the Mean, Median, and Mode for the above data.

What does this information tell you about students' performance?

MORE PRACTICE

The owner of a shoe shop recorded the sizes of the feet of all the

customers who bought shoes in his shop in one morning. These

sizes are listed below:

8, 7, 4, 5, 9, 13, 10, 8, 8, 7, 6, 5, 3, 11, 10, 8, 5, 4, 8, 6Find the mean, median, mode and range.


14/15

Choosing an Appropriate Measure of Central Tendency

The mean is normally the preferred measure of centraltendency. However, there are situations in which the mean isnot the best measure:

1. For a random distribution of data, themean is preferred.Examples:Students' heights in a classroomTemperature over a length of time

2. For a skewed data set, a median is more appropriate than amean. The skewed data set (extreme data points) will cause themean value to be much more extreme than the median, andtherefore less central.

Examples:Income of a group of peopleTest scores for a group of students

3. The mode can be used for non-numerical data.Examples: The most common...The most common hair color in a roomFinding the most common car in a parking lot


15/15

LEARNING LOG - Gerald - 7.S.4/5

Gerald isn't sure how to find the mean, median, mode, orrange of the following set of data: 13, 19, 15,17, 16, 21, 20,

14, 15, 23, 17, 14, 25, 24, 13, and 17. Show and explain.

LESSON 30 - Central Tendency

Documents

Transcript of LESSON 30 - Central Tendency