Table of Contents1. Standard Deviation

1. Standard Deviation

Essential Question – What is standard deviation and what

does it measure?

Measures of Central Tendency are…

Mean - average Median – the middle number Mode – the number that is there the

most

Measures of Variability

Tell you how far apart or how spread out the data is Range = biggest – smallest Interquartile range (IQR) = Q3 – Q1 (the

middle 50% of the data) Variance Standard Deviation

Five-number summary

The five-number summary is the Mean Median Mode Variance Standard deviation

Formulas

We will now be writing the mean with a new formula

xx

n

X bar means “mean” sum

Numberof terms

Variance

2

2

( )x x

n

Standard Deviation

Standard Deviation is the square root of variance

2( )x x

n

Mean is the average

To find the mean of the high temperatures in a week which are:

80, 78, 81, 83, 76, 82, and 801st Add all the numbers2nd Count all the numbers you have.3rd Divide the total by the

number of numbers that you have.

Median is the middle number

To find the median of the high temperatures in a week, which were:

80, 78, 81, 83, 76, 82, and 801st Write the numbers in order from

smallest to largest.2nd Count the numbers and find the

middle one. If you have an even number, then average the two middle numbers.

Mode is the most frequently occurring number

To find the mode of the high temperatures in a week, which were:

80, 78, 81, 83, 76, 82, and 801st Write the numbers in order from smallest to largest.2nd Look for the number that appears the most number of times.

To Make a box and whisker plot:

1st Find the median, Q1, and Q3

76 78 80 80 81 82 83

To Make a box and whisker plot:

2nd Find the lower and upper extreme. 76 78 80 80 81 82 83

3rd Draw a number line that has scale greater than the range of the given numbers.

8476 77 81807978 82 83

To Make a box and whisker plot:

3rd Put the points above the number line at the lower extreme, the lower quartile, the median, the upper quartile, and the upper extreme.

76 77 81807978 82 83

To Make a box and whisker plot:

4th Draw a box around the lower and upper quartiles and a vertical line through the box where the median is located.

76 77 81807978 82 83

To Make a box and whisker plot:

5th Run whiskers from the box to the lower and upper extreme.

76 77 81807978 82 83

Box and Whisker Plot

Each sections of a box and whisker plot contains 25% of the data

Steps to calculate variance

Find the mean Subtract each data point from the

mean Square each of these numbers Add these all up Divide by the number of terms Making a table is helpful!

Example

Find the variance 4, 5, 6, 7, 8

Example

Find the variance 2, 4, 6, 8, 10

Example

Find the standard deviation 4, 5, 6, 7, 8