1. 0-12: Measures of center, variation, and position

2. 0-12: Center, Variation, and Position
Quantitative Data: Data that has units and can be measured (numerical)
Ex: Times for a race, ages of people, Distances
Qualitative Data: Data that can be organized into categories
Favorite color, hair color, phone numbers

3. 0-12: Center, Variation, and Position
Mean:
Use the mean to describe the middle of a set of data that DOES NOT have an outlier. An outlier is a data value that is much higher or lower than the other data values in the set.
Median: Middle value in the set when the numbers are arranged in order.
If a set has an even number of values, the median is the average of the two middle numbers.
Use the median to describe the middle of a data set that DOES have an outlier.
Mode: The data item that occurs the most times
Can have 0, 1, or more than one modes

4. 0-12: Center, Variation, and Position
Example 1: The table shows the number of hits Marcus made for his baseball team. Find the mean, median and mode.
Mean
26 hits in 6 games
26/6 ≈ 4.3 hits
Median
Put numbers in order: 2, 3, 3, 5, 6, 7
Average two middle numbers
3 + 5/2 = 8/2 = 4 hits
Mode
Number that shows up most often
3 hits

5. 0-12: Center, Variation, and Position
Variation: A measure of spread that shows how widely data values vary
Range: Largest value minus smallest value of a set
Example 2: It took Olivia 18, 15, 15, 12, and 14 minutes to walk to school each day. Find the range.
Range = biggest – smallest
= 18 – 12 = 6 minutes

6. 0-12: Center, Variation, and Position
Quartiles: A measure of position that divides data into four equal sized groups.
The median marks the second quartile (Q2)
The lower quartile (Q1) is the median of the lower half
The upper quartile (Q3) is the median of the upper half
Five-number summary: The minimum, three quartiles, and maximum of a data set.

7. 0-12: Center, Variation, and Position
Example 3
The number of boxes of donuts sold for a fundraiser each day for the last 11 days were 22, 16, 35, 26, 14, 17, 28, 29, 21, 17, and 20. Find the five-number summary of this data set.
Put all numbers in order
14, 16, 17, 17, 20, 21, 22, 26, 28, 29, 35
Find the median of the data set
Use the data to the left/right of the median to find the lower/upper quartiles
Find the minimum/maximum
The minimum is 14, the lower quartile is 17, the median is 21, the upper quartile is 28 and the maximum is 35

8. 0-12: Center, Variation, and Position
The difference between the upper and lower quartile is called the interquartile range
14, 16, 17, 17, 20, 21, 22, 26, 28, 29, 35
The interquartile range is 28 – 17 = 11
Outlier: An extremely high or extremely low value when compared with the rest of the set. Outlier data will be more than 1.5 times the interquartile range.

9. 0-12: Center, Variation, and Position
Example 4: Finding an outlier
Students taking a make-up test received the following scores: 88, 79, 94, 90, 45, 71, 82, 88
Identify any outliers
Determine Q1 and Q3
45, 71, 79, 82, 88, 88, 90, 94
Interquartile range: 89 – 75 = 14
Any outliers will be smaller than Q1 – 1.5(IQR) or bigger than Q (IQR)
75 – 1.5(14) = 54
(14) = 110
The outlier is 45 (because it’s smaller than 54)
Q1 = 75
Q3 = 89
Q2 = 85

10. 0-12: Center, Variation, and Position
Assignment
Page P39-P40
1 – 17, odds