Best Measure of Center & Balance Point

Best Measure of Center

Mean is the balance point of the data

• Mean is the average, so add up all the numbers then divide

• Mean is typically the best measure of center **unless there is an outlier**

• EX: {2, 3, 8, 9, 9} = 2 + 3 + 8 + 9 + 9 = 31 ÷  5 = 6.2

Open Ended

What do you think the word "outlier" means?

What are Outliers?

• An extreme high or low number in the data

• Outliers stick out far from the rest of the numbers, kind of like an "outsider"

• Outliers affect the mean (average)

• EX: grades: 92%, 90%, 89%, 88%, 88%, 65%

Median = middle

• Median is the middle when the data is ordered least to greatest

• * Always order your numbers first, then find the middle number*

• EX: {9, 3, 8, 9, 2}  =  2, 3, 8, 9, 9  = 8 is the median

Poll

When finding the median, what do you do if there are two numbers in the middle?

• pick one of them

• subtract the two

• find the average of the two

• add the two

When Finding the Median, What Happens When There Are Two Numbers in the Middle?

• Find the mean (average) of the two numbers

• EX: 2, 3, 7, 8, 9, 9    =    7 + 8  =       15 $\div$  2  =  7.5

Mode = Most Often

• Mode is when a piece of data appears a lot OR when the data is not numbers

• EX: 25, 29, 25, 25, 27, 23, 25, 25

• EX: strawberry, strawberry, cherry, lemon, strawberry, orange, strawberry, cherry, strawberry

Best Measure of Center

When There's An Outlier

• If there is NO outlier, the best measure of center to use is the mean

• EX: 12, 11, 8, 6, 11, 7, 10 = mean

• If there is an outlier, the best measure of center to use is the median

• EX: 12, 11, 8, 6, 11, 30, 10 = median

Range = Difference Between Highest & Lowest Values

• Range - Subtract the highest and lowest values

• Ex: {1, 2, 3, 5, 7, 9} = 9 - 1 = 8

• **NEVER choose the range when asked what is the best measure of center**

Multiple Choice

Are there any outliers in the following data set?

6, 12, 14, 8, 6, 12, 19

• Yes

• No

Multiple Choice

What is the best measure of center?

6, 12, 14, 8, 6, 12, 19

• mean

• median

• mode

• range

Multiple Choice

Are there any outliers in the following data set?

15, 17, 18, 1, 22

• Yes

• No

Multiple Choice

What is the best measure of center?

15, 17, 18, 1, 22

• mean

• median

• mode

• range

Multiple Choice

Are there any outliers in the following data set?

23, 10, 22, 25, 13, 15, 23, 22

• Yes

• No

Multiple Choice

What is the best measure of center?

23, 10, 22, 25, 13, 15, 23, 22

• mean

• median

• mode

• range

Multiple Choice

What is an outlier?

• number that repeats often

• the average of a data set

• the difference from the highest and lowest numbers

• an extreme high or low number

Multiple Choice

For which data set is the mode most useful?

• {8, 12, 8, 14, 14, 20}

• {1, 2, 3, 4, 5}

• {4, 4, 6, 6, 8, 8}

• {32, 36, 41, 36, 40, 36}

Multiple Choice

For which data set is the mean the best measure of center to use?

• {94, 96, 98, 100, 97}

• {54, 60, 58, 3, 64}

• {26, 29, 71, 28, 71}

• {5, 5, 5, 301, 5}

Multiple Choice

Mr. Magnaro owns a sandwich shop that sells 10 different sandwiches. He takes a survey of 50 people to find out their favorite sandwich. Which measure of center should he use to determine the most popular sandwich?

• mean

• median

• mode

• range

Multiple Choice

The number of text messages sent by Carolyn each day from Monday to Friday is shown below.

1, 3, 2, 26, 3

Which measure best describes the data set?

• mean

• median

• mode

• range

*IMPORTANT* Things to Remember!

• NO outlier = mean is the best measure of center to use

• An outlier = median is the best measure of center to use

• number repeating a lot OR no numbers in the data = mode is the best measure to use

• *NEVER USE RANGE* as the best measure to use

How to Find the Balance Point

• EX: What is the Balance Point of the following data set?: {5, 3, 9, 4, 2, 7}

• Balance Point = Mean = Average

• ADD: 5 + 3 + 9 + 4 + 2 + 7 = ?

• = 30, then DIVIDE by amount of numbers

• 30 / 6 = ?

• Balance Point = 5

Finding Balance Point from a Line Plot

• An "X" represents a number in the data.

• Follow steps: ADD: 16 + 17 + 18 + 18 + 18 + 21 + 22 + 22 = ?

• = 152, then DIVIDE by the amount of "X"s

• 152 / 8 = ?

• Balance Point = 19

• 
  

Multiple Choice

Find the Balance Point of the following data: {1, 6, 6, 1, 10, 8, 0, 12, 1}

• 7

• 45

• 5

• 4

• 6

Multiple Choice

Find the Balance Point of the data in the line plot.

• 56

• 14

• 4

• 5.6

Fill in the Blanks