Shape, Center, Spread

Measures of Center & Spread

Mean

"Average" of a set of numbers

​To calculate it:

1. Add up all the numbers in the data set.

2. Divide ​that total by the amount of numbers in the data set.

Mean Examples

Multiple Choice

Find the mean of these numbers:

2, 57, 38, 42, 6

• 29

• 38

• 50

• 145

Multiple Choice

Find the mean for these test scores:

67, 74, 95, 98, 98, 99, 102

• 90.4

• 633

• 98

• 92.3

Median

"Middle" number of a sorted list of numbers

​To calculate it:

1. Write the numbers in order from least to greatest.

2. Find the middle number.

3. If there are 2 "middle" numbers, the median will be the mean of those 2 numbers.

Median Examples

Multiple Choice

Find the median from the list of numbers:

60, 58, 52, 48, 60

• 58

• 59

• 60

• 118

Multiple Choice

What is the median of this set of data?
10, 90, 80, 60, 50, 40, 70, 30, 20, 100

• 50
• 60
• 55
• 45

Range

Difference between the largest & smallest values

in a set

​To calculate it:

1. Write the numbers in order from least to greatest.

2. Subtract (range = largest value – smallest value)

Range Example

Multiple Choice

Find the range.
12, 5, 9, 18, 22, 25, 5

• 20
• 15
• 22
• 18

Multiple Choice

Find the range of the data.

16, 28, 6, 19, 21, 15, 22, 33, 17

• 18

• 27

• 30

• 12

Quartiles

Divides the data in 4 equal parts

• 1st Quartile (Q1): the middle of the lower half of the data set

​

• 3rd Quartile (Q3): the middle of the upper half of the data set

Quartile Examples

Multiple Choice

Find the 1st Quartile (Q1) of the following data set:

2, 3, 4, 5, 5, 5, 7

• 4

• 6

• 3

• 5

Multiple Choice

Find the 3rd Quartile (Q3) of these numbers:

2, 3, 4, 5, 5, 5, 7

• 4

• 6

• 3

• 5

Interquartile Range (IQR)

Middle 50% of values when ordered from lowest to highest

​To calculate it:

1. Put the numbers in order from least to greatest.

2. Find the median.

3. Find the median of the lower and upper half of the data. These values are quartile 1 (Q1) and quartile 3 (Q3).

4. Find the difference between Q3 and Q1. (IQR = Q3 – Q1)

IQR Example

Multiple Choice

Find the IQR of the data.

20, 22, 25, 29, 31

• 30
• 21
• 25
• 9

Mean Absolute Deviation (MAD)

Measure of variation in a set of data (how far the data is away from the mean on average)

​To calculate it:

1. Find the mean of the numbers.

2. Calculate the difference between each number and the mean.

3. Take the absolute value of the differences.

4. Calculate the mean (average) of the absolute values.

MAD Example

Multiple Choice

Find the MAD of the following data:

14, 17, 18, 22, 24

• 19

• 3.2

• 2.3

• 23

Multiple Choice

• mean

• median

• range

• standard deviation

Multiple Choice

• Class A has B higher median than Class B, and Class B has a higher mean than Class A

• Class B has a higher median than Class A and Class B has a higher mean than Class B

• Class A and B have the same median, and Class B has a lower mean than Class A

• Class A and B have the same median, and Class A has a lower mean than Class B

Multiple Choice

• Since the percentages do not add up to 100, any poll results are invalid

• Those who responded to the poll are not a random sample of the United States

• There were not 50% 'Yes' responses and 50% 'No' responses

• The show did not allow viewers enough time to respond to the poll

Multiple Choice

• Residents of California are more likely to leave the state than residents of Rhode Island

• Residents of California are more likely not to have been born in-state than residents of Rhode Island

• Residents of California are more likely to travel internationally than Residents of Rhode Island

• Residents of California are more likely to have been born in another country or US state than to have been born in-state

Multiple Choice

• The mode of this data set is 3 hours

• The mean of the data set is 2.75 hours

• Exactly 60% of the students surveyed use the internet 3 to 4 hours a day

• The median is smaller than the mean for this data set

Multiple Choice

• 45

• 30

• 15

• 5

Multiple Choice

• 190

• 233

• 265

• 390

Multiple Choice

• 3

• 3.5

• 4.25

• 10

Multiple Choice

• 84,000

• 105,000

• 189,000

• 218,000

Multiple Choice

• $$s_1=s_{2\ }and\ r_1=r_2$$

• $$s_1<s_{2\ }and\ r_1<r_2$$

• $$s_1>s_{2\ }and\ r_1>r_2$$

• $$s_1\ne s_{2\ }and\ r_1=r_2$$