0-12: MEASURES OF CENTER, VARIATION, AND POSITION

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

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

sum of the data items

total number of data items

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

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

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.

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

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.

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 Q3 + 1.5(IQR) 75 – 1.5(14) = 54 89 + 1.5(14) = 110

The outlier is 45 (because it’s smaller than 54)

Q2 = 85Q3 = 89Q1 = 75

0-12: Center, Variation, and Position Assignment

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