1. Table of Contents 1. Standard Deviation

2. 1. Standard Deviation
Essential Question – What is standard deviation and what does it measure?

3. Measures of Central Tendency are…
Mean - average
Median – the middle number
Mode – the number that is there the most

4. 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

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

6. Formulas We will now be writing the mean with a new formula Number
of terms
X bar means “mean”
sum

7. Variance

8. Standard Deviation
Standard Deviation is the square root of variance

9. 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.

10. 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.

11. 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.

12. To Make a box and whisker plot:
1st Find the median, Q1, and Q3

13. To Make a box and whisker plot:
2nd Find the lower and upper extreme.
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

14. 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

15. 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

16. 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

17. Box and Whisker Plot
Each sections of a box and whisker plot contains 25% of the data

18. 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!

19. Example
Find the variance 4, 5, 6, 7, 8

20. Example
Find the variance 2, 4, 6, 8, 10

21. Example
Find the standard deviation 4, 5, 6, 7, 8