Table of Contents 1. 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 Number of terms X bar means “mean” sum

Variance

Standard Deviation Standard Deviation is the square root of variance

Mean is the average To find the mean of the high temperatures in a week which are: 80, 78, 81, 83, 76, 82, and 80 1st Add all the numbers 2nd 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 80 1st 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 80 1st 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. 84 76 77 81 80 79 78 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 81 80 79 78 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 81 80 79 78 82 83

To Make a box and whisker plot: 5th Run whiskers from the box to the lower and upper extreme. 76 77 81 80 79 78 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