Measure of Center

Measure of Center

by Zanier Fuller

​What is the measure of center?

• A single value used to represent a set of data.

• ​It is often referred to the "typical" value.

• ​The most common measures of center is MEAN & MEDIAN.

​The MEAN of the data

​How to caluclate mean.

​

​1) add all the values in the data set.

​

​2) Divide the sum by the # of values in the data set.

​The MEDIAN of the data

​How to caluclate median.

​

​1) orgainze data in ascending or descending order.

​2) The median is the value that falls in the middle.

​

​

***** when two numbers fall in the middle, add them and divide by 2

Multiple Choice

What is the mean of these numbers?
4,5,5,2,3,3,2,8

• 40
• 24
• 4
• 256

Multiple Choice

Find the median:
3, 5, 7, 4, 3, 1

• 3 and 4
• There isn't one
• 3.5
• 3

Multiple Choice

1. Find the average (mean) of these numbers.
10, 3, 2, 5

• 5
• 4
• 10
• 3

Multiple Choice

To find the average of a set of numbers, add up all the items and divide by...

• 2
• The minimum
• The maximum
• The number of items

​Why is knowing the MEAN & MEDIAN important?

Multiple Choice

Which of the following is the best measure of center?

• MEAN

• MEDIAN

• ANYONE COULD WORK

​OUTLIER

​An outlier is a data point that differs greatly from the entire data set.

​

​What is the outlier for this data set?

​

​Whenever a data set includes an outlier, the median is the best measure of center.

Fill in the Blank

Which number from the data set 1, 1, 1, 2, 2, 3, 4, 5, 5, and 25 is an outlier?

Multiple Choice

Which measure of center best represents this set of data?
12, 13, 11, 16, 31, 14, 10, 15

• Mean
• median
• mode

Multiple Choice

The salary of the employees in the office were $15,000; $18,000; $16,000; $14,000; $90,000; and $17,000.  What is the best measure of the central tendency of the salaries?

• Mean
• Median
• Mode
• Range

Multiple Choice

What measure of center is best to use when we have outliers?

• mean

• median

• mode

• range

Multiple Choice

When analyzing numerical data, the best measure of center with NO outlier is:

• mean

• median

• mode

• range

Multiple Choice

When analyzing numerical data, the best measure of center with an outlier is:

• mean

• median

• mode

• range

Multiple Choice

Which is the MIDDLE?

• Mean
• Median
• Mode
• Range

Multiple Choice

The average number is

• mean

• median

• mode

• range

Multiple Choice

The data value that occurs the most

• Mean
• Median
• Mode
• Range

Multiple Choice

How many scores are listed in this Stem and Leaf Plot?

• 3
• 6
• 9
• 18

Multiple Choice

Which measures are affected by the outlier? (you need to find the mean, median, and mode without the outlier to answer this)

• mean

• mean and median

• mean, median, and mode

• median

Multiple Choice

What did the outlier do to the mean and median in the data set 1, 1, 1, 2, 2, 3, 4, 5, 5, and 25?

• Nothing

• They were both greater with the outlier.

• They were both less with the outlier.

Multiple Choice

What is the most appropriate measure of center for the following data set?
3, 90, 92, 91, 94, 99, 95

• Mean
• Median
• Mode
• Range

Multiple Choice

Your math grades are 90, 85, 58, 90, 80, 100, and 90.  Which grade is the outlier?

• 90
• 58

​But How exactly will the outlier impact the data?

​Will it make the mean larger or smaller?

​

​

How do you know?

Multiple Choice

The data set below has an outlier of 42.
2, 5, 12, 15, 19, 4, 6, 11, 16, 18, 12, 12, 42
What effect does removing the outlier have on the distribution of the data?

• The mean will decrease
• The median will decrease
• The mean will increase
• The median will increase

Multiple Choice

The interquartile range (IQR) of a data set is the difference between the third and first quartiles. It represents the range of the middle half of the data.

• True
• False

Multiple Choice

Ms. Rork's class had a range of test grades from 78 to 97. She forgot to add in a student who got an 80% on the test. How will this affect the range?

• Increase
• Decrease
• Stay the Same

Multiple Choice

Mrs. Rosenblatt's class has an average grade of 87. Later on she realizes she left out Joe's score. His grade was a 65. The new mean will ,....

• increase
• decrease
• stay the same

Multiple Choice

Data values that are far away from most of the other data in a set...

• Gaps

• Outliers

• Averages

• Clusters

Multiple Select

The Measures of Center are.....

• IQR

• Mean

• Median

• Range

Multiple Choice

What is the the first quartile for the data on the 6TH Grade Math Test?

• 68

• 78

• 85

• 93

Multiple Choice

What is the the third quartile for the data on the 6TH Grade Math Test?

• 68

• 78

• 85

• 93

Multiple Choice

What is the maximum score on the 6TH Grade Math Test?

• 78

• 85

• 93

• 97

Multiple Choice

What is the median on this box pot?

• 20

• 30

• 62

• 70

Multiple Choice

What is the interquartile range for this box plot? Remember to subtract the first quartile from the third quartile.

• 10

• 32

• 40

• 72

Multiple Choice

A value that is much higher or much lower than the other values in a set of data.

• Outlier

• Mean

• Median

• Mode

Multiple Choice

Your math grades are 90, 85, 0, 90, 80, 100, and 90. Which grade is the outlier?

• 90

• 0

• 80

• 100

Multiple Choice

Gabriella’s quiz grades are shown below.
88, 92, 92, 96, 98
Gabriella scored a 20 on her sixth quiz. What effect does this score have?

• The low score causes the median to increase.
• The low score causes the median to decrease.
• The low score causes the mean to increase.
• The low score causes the mean to decrease.

Multiple Choice

If 20 is added to the data set below, which statement will be true?
50, 55, 55, 60, 62

• The median will be 20
• The mode will increase
• The mean will increase
• The mean will decrease

Multiple Choice

The data below represent the ages of several people in a class.What effect does Mr. Smith’s age have on the data set?

• Mr. Smith’s age increases the mode of the data.
• Mr. Smith’s age decreases the mean of the data.
• Mr. Smith’s age increases the mean of the data.
• Mr. Smith’s age increases the median of the data.

Multiple Choice

The table below shows the lengths of fences a company installed during a week. 
Which statement is true?

• The 275-foot fence caused the mean to be significantly lower than the median.
• The 275-foot fence caused the median to be significantly lower than the mean.
• The 2,250-foot fence caused the mean to be significantly greater than the median.
• The 2,250-foot fence caused the median to be significantly greater than the mean.

Multiple Choice

A realtor wants to give a customer an idea of housing prices in a neighborhood. All the houses are priced within $20,000 of one another, except one house that is much larger and more expensive than the rest. Which measure(s) of central tendency will be most affected by the one expensive house?

• Mode only
• Mean only
• Both mode and mean
• Both mean and median

Multiple Choice

The hourly salaries of the workers at a restaurant are shown below.
$7.75, $8.50, $7.25, $9.00, $30.00, $8.25, $7.75, $9.00
Which statement is true?

• The worker who earns $7.25 an hour causes the mean to be a better representation of the typical salary than the median.
• The worker who earns $7.25 an hour causes the median to be  a better representation of typical salary than the mean.
• The worker who earns $30.00 an hour causes the mean to be a better representation of the typical salary than the median.
• The worker who earns $30.00 an hour causes the median to be a better representation of the typical salary than the mean.