COMPUTATIONAL FORMULAS AND IQR’S

Compare the following heights in inches:

Boys Girls72 6174 6470 6568 6669 6870 6768 6569 6367 6270 6571 66  67  64  66

Objective•Calculate standard deviation, variance and IQR.

Relevance•To be able to analyze a set of data and see how far each value is above or below the mean of the set.

Computational Formula• This is an easier computational formula that contains no rounding.

1

22

2

n

nxx

s

Example – Find Var and St Dev

7

8

22

34

42

496448411561764

113 x 35172 x

8.240451133517

1

222

2

n

nxx

s 5.158.240 s

You Try One!

48

1218223438

166414432448411561444

136 x

95.164

671363632

1

222

2

nnxx

s

36322 x

8.1295.164 s

Is the standard deviation affected by outliers?

5

7

5

8

9

5

7

5

8

29

The standard deviation IS sensitive to extreme values.

67656870746061646768

The following data represents the heights of some students in my class.

a. Find the mean & standard deviation.

b. What % are within 1 standard deviation of the mean? ()

c. What % are within 2 standard deviations f the mean? ()

14.4s4.66x

54.7014.44.6626.6214.44.66

:1

sx

%70107

68.7412.58:2 sx

%1001010

IQR – Interquartile Range

•This is the measure of variability that is not affected by outliers.

• It is based on quartiles.

25%25% 25%

25%

1Q 2Q 3Q

1Q

2Q

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

3Q

- This is the median.

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

3 1IQR Q Q

18 24 25 27 27 29 30 33 34) )( (Q1 = 24.5 Q3 = 31.5

IQR = 31.5 – 24.5 = 7

Find IQR

12 13 16 18 22 24 27 40

Q1 = 14.5 Q3 = 25.5

IQR = 25.5 – 14.5 = 11

Find IQR8 10 11 14 16 20 22 26 28 32

IQR = 15

Find IQR4 5 6 6 7 10 22

IQR = 15

If normal distribution – then you can estimate the standard deviation with the IQR.

*Can also be use to check to see if a distribution is normal – if much larger then it’s skewed.

Standard Deviation =

Which Measure Should You Report?

Shape Central Tendency

Dispersion(Spread)

Symmetric Mean Standard Deviation

Skewed Left or Right

Median IQR

NOTE: When told to “describe the distribution” you will give the shape, the center and the spread of the distribution using the above categories as a guideline.

Homework• Worksheet

• Use the new formula to compute the standard deviation.

• Now – time for the lab!