Standard Deviaton

Standard deviation

Although the mean, median, and mode are fairly easy to understand, they do not measure how a set of data (distribution) varies. i.e. are the numbers are bunched close together or are they spread apart?

e.g.1 Christina drives to school and can follow either the Brooks Expressway or the Kingston Expressway. She timed herself for two weeks and got the following figures. Brooks 15,26,30,39,45 Kingston 29,30,3l,32,33

Which would you drive? Why?

Find the mean and median of each road

1 Find the mean of the Brooks

Brooks 15,26,30,39,45 Kingston 29,30,31,32,33

2 Find the median of the Brooks

Brooks 15,26,30,39,45 Kingston 29,30,31,32,33

3 Find the mean of the Kingston.

Brooks 15,26,30,39,45 Kingston 29,30,31,32,33

4 Find the median of the Kingston.

Brooks 15,26,30,39,45 Kingston 29,30,31,32,33

5 so which way is better?

A Brooks

B Kingston

Brooks 15,26,30,39,45 Kingston 29,30,31,32,33

On the Brooks the time varied from 15 - 45 minutes. On the Kingston the time varied from 29 - 33

6 We say that the Brooks' range is __ minutes

This range is useful in some instances but may be affected strongly by an extreme value.

The range is the difference between the largest and smallest numbers.

e.g. suppose one day on the Kingston she got caught in a traffic jam and spent a whole hour.

Even though all the other days were close together, the range would be very high.

Variability refers to how spread out the data is. In the above example the Brooks variability would be very ___________ , while the Kingston's would be _____________ .

The standard deviation is a numerical measurement of a set of data's variability.

A larger standard deviation means that the

A low standard deviation means it is

To find standard deviation

Enter Brooks 15,26,30,39,45 into L1 of your calculator and Kingston 29,30,31,32,33 into L2.

Do 1 vars stats on L1 then L2.

L1 s = 10.41 L2 s = 1.41

7 which data set would you expect a higher standard deviation?

A Student's age in the class

B Student's mark in the class

e.g.2

e.g. 3 Which types of products require a low standard deviation?

·diameter of oranges·iPod battery life·diameter of a bolt·mass of a bag of chips·amount of ibuprofen in a pill·student marks·number of cheerios in a box

E.g. 4 A machine packaging candy in 90-g packages is thought to be faulty. A sample of packages is selected and the actual masses in grams are as follows.

86,91,89,92,90,93,90,90,91,88

If the machine is working properly, the standard deviation must be less than 1.3. What is this machine's standard deviation? Is it faulty?

8 What is the standard deviation? (1 decimal place)

.

e.g. 5 Which of the following histograms has the higher standard deviation?

A B

Why? How can you tell? Is there anyway to calculate?