Best Measure of Center & Balance Point

Presentation

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Mathematics

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6th Grade

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Practice Problem

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Medium

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CCSS

6.SP.B.5D, 6.SP.A.3, 6.SP.B.5C

Standards-aligned

Mrs. A. Leonard

Used 124+ times

FREE Resource

12 Slides • 16 Questions

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?

Type response here

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

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

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

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}

Multiple Choice

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

5.6

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