Interquartile Range Powerpoint.pptx

INTERQUARTILE

RANGE

Objectives –

Measures of Variation

• _{Measures of Center describe the values most typical of}

a data set

• _{The mean, median, and mode are measures of center}

• _{Measures of Variation describe how the numbers in the}

data set are distributed (spread out)

• _{The range, interquartile range, and mean absolute deviation are}

measures of spread

• _{Good measures of center/spread are not affected by}

outliers

• _{Remember outliers are values that are very large or very small in}

Review of Mean, Median, Mode, Range

Mean = 7 + 5 + 2 + 7 + 6 + 12 + 10 + 4 + 8 + 9

₁₀ = 70

10 = 7

Range = 12 – 2 = 10

Example 1. Two dice were thrown 10 times and their scores were added together and recorded. Find the mean and range for this data.

7, 5, 2, 7, 6, 12, 10, 4, 8, 9

Median = 2 ,4, 5, 6, 7, 7, 8, 9, 10, 12 = 7 + 7 2

= 7

Mode = 2 ,4, 5, 6, 7, 7, 8, 9, 10, 12 = 7

(biggest – smallest) (the most frequent)

Affect of Outliers

• _{Outliers are values in the data set that are extreme}

(much bigger or smaller than the rest of the data)

• _{Outliers affect the mean and the range, but not the}

median and mode

Example 2. What if the same data as example 1 included the outlier 106

7, 5, 2, 7, 6, 12, 10, 4, 8, 9, 106

Mean – 7 + 5 + 2 + 7 + 6 + 12 + 10 + 4 + 8 + 9 + 106 = 176 = 16

11 11

Median = 2 ,4, 5, 6, 7, 7, 8, 9, 10, 12, 105 = 7 _{Mode = 2 ,4, 5, 6, 7, 7, 8, 9, 10, 12, 105 = 7}

Range = 105 – 2 = 103

Instead of 7 the mean is

now 16

Instead of 10 the range is

now 103

Good Measures

• _{Good measures of center & spread are not affected by}

outliers

• _{As we saw in the previous example, the mean and the}

range are affected by outliers (especially the range)

• _{In most cases, the median and mode are not affected by}

outliers which makes them better measures of center (or spread)

• _{The interquartile range relies on calculating medians, so it}

Single middle value

The Median – A Closer Look

The median is the middle value of a set of data once the data has been ordered.

Example 1. Robert hit 11 balls at Grimsby driving range. The recorded distances of his drives, measured in yards, are given below. Find the median distance for his drives.

85, 125, 130, 65, 100, 70, 75, 50, 140, 95, 70

Median drive = 85 yards

50, 65, 70, 70, 75, 85, 95, 100, 125, 130, 140

Two middle values so take the mean. 80+95

2

Example 2. Robert hit 12 balls at Grimsby driving range. The recorded distances of his drives, measured in yards, are given below. Find the median distance for his drives.

85, 125, 130, 65, 100, 70, 75, 50, 140, 135, 95, 70

Median drive = 90 yards

50, 65, 70, 70, 75, 85, 95, 100, 125, 130, 135, 140

Ordered data

The Median – A Closer Look

IQR – Interquartile Range

• _{The interquartile range (IQR) is the difference (or}

range) between the upper (Q3) and lower (Q1) quartiles, and describes the middle 50% of values

when ordered from lowest to highest.

• _{The IQR is often seen as a better measure of spread}

than the range as it is not affected by outliers.

•

_{It is based on}

_quartiles

_.

25% 25% 25% 25%

- This is the median of the lower ½ of the sample.

- This is the median of all the data.

- This is the median of the upper ½ of the sample.

Quartiles

1

Q

Q

Q

1

Q

2

Q

3

How to find the Interquartile Range

Steps:

1. Order the data from least to greatest

2. Find the median (middle #). Remember if there are 2

middle #s add, then divide by 2

3. Put parentheses (or brackets) around the upper and

lower half of the data

• _{All #s below the median are the lower half, all #s above the median}

are the upper half

4. Find quartile 1 and quartile 3

• _{The median of the lower half will be quartile 1} • _{The median of the upper half will be quartile 3}

18 24 25 27 27 29 30 33 34

)

)

(

(

Q1 = 24.5 Q3 = 31.5

IQR = 31.5 – 24.5 = 7

Median (Q2)

This is the median of the lower

half.

This is the median of the upper

half.

3

1

Find IQR

12 13 16 18 22 24 27 40

Q1 = 14.5 Q3 = 25.5

IQR = 25.5 – 14.5 = 11

Median (Q2) =

= 20 2

13 + 16 = 14.5

2 24 + 27 = 25.5

Your Turn #1 - Find IQR

8

10 11 14 16 20 22 26 28 32

Awesome – These data are already in order from least to

Your Turn #1 - Find IQR

8

10

11

14 16 20 22

26

28 32

IQR = 15

Q1 = 11 _{Median (Q2) =} Q3 = 26

= 18 2

This is the median of the lower

half.

This is the median of the upper

half.

Your Turn #2 - Find IQR

Your Turn #2 - Find IQR

4

5

6

6

7

10

22

IQR = 5

Put the data in order from L-G first

Median (Q2) =6

Q1 = 5 Q3 = 10

Your Turn #3 - Find IQR

Your Turn #3 - Find IQR

38 46

55

56 58 59 61

65

67 75

Put the data in order from L-G first

Median (Q2) =

= 58.5 2

Q1 = 55 Q3 = 65

IQR = 65-55 = 10