1. Warm Up
Find the mean, median, mode, and range of the following set of data.
3, 4, 5, 5, 8, 9, 12, 14
Mean =
Median =
Mode =
Range =

2. Test and Homework Review

3. What are measures of spread?
Math II B Day 2 (1-5-11)
Standard MM2D1B
Understand and calculate the means and standard deviations of sets of data
Today’s Question:
What are measures of spread?
How do we calculate standard deviation and what does it mean?

4. Welcome to the wonderful world of Statistics

5. Some quotes on Statistics
"There are three kinds of lies: lies, damned lies and statistics." - Mark Twain
“65% of all statistics are made up. Including this one" - Dilbert
There are two kinds of statistics, the kind you look up and the kind you make up. 
- Rex Stout

6. Describing Data

7. Ways to look at the data Box plot Dot plot Histogram
Number of hurricanes that occurred each year from 1944
through 2000 as reported by Science magazine

8. 3 Characteristics of data
Shape
Center
Spread

9. Shape of the data – Symmetric
The IQ scores of 60 randomly selected 5th graders

10. Shape of the data – Symmetric
The age of all US Presidents at the time they took office
Notice that this distribution has only one mode

11. Shape of the data – Bimodal
The winning times in the Kentucky Derby from 1875 to the
present. Why two modes?
The length of the track was reduced from 1.5 miles to
1.25 miles in The race officials thought that 1.5 miles
was too far.

12. Shape of the data – skewed
LEFT
RIGHT
Data for two different variables for all female heart attack
patients in New York state in one year. One is skewed
left; the other is skewed right. Which is which?

13. Center and Spread of Data
Maximum Q3
Median Q1
Minimum
100th percentile
75th percentile
50th percentile
25th percentile
0th percentile
These numbers are called the 5 number summary.
The median measures the center of the data.
Q3 – Q1 = Interquartile range (IQR) measures the spread.

14. Recall the box and whisker

15. Create a Box and Whisker for both cities
Miami weather
76,78,81,84,87,90,91,91,89,85,81,78
Atlanta weather
50,55,63,71,78,84,88,86,81,72,62,53

16. Temperatures in 3 cities
Which city’s temperatures are the
1. most spread out ?
2. most consistent ?

17. You try….. Which salesperson is more consistent and why?

18. Measures of Central Tendency and Dispersion
Central Tendency: Mean, Median, and Mode
Dispersion or Spread: Range, IQR, Standard Deviation, and Variance
Examples of Uses for Standard Deviation and Variance:
Factory Processes
Stocks
Weather
Sports Teams
Grades
Attendance to events
?????

19. What are Variance and Standard Deviation

20. Symbols Symbols: s2 = Sample Variance s = Sample Standard Deviation
10/12/2019
Symbols
Symbols:
s2 = Sample Variance
s = Sample Standard Deviation
2 = Population Variance
 = Population Standard Deviation
x = Mean -- 20

21. Center and spread of data
The square root of the variance. This quantity has the same
units as the data. This is one of the most common measures
of the spread of a distribution.
The formula given above is for the population standard
deviation.

22. Center and spread of data
Mean
Absolute
Deviation
Standard
Deviation
Variance

23. 2, 6, 7, 8, 9, 16 sum them up = 106 N = 6 Variance =106/6 = 17.67X 2 6 7 8 9 16
(x-xbar) -6 -2 -1 1 8
(x-xbar)2
(-6) 2 = 36
(-2) 2 = 4
(-1) 2 = 1
(0) 2 = 0
(1) 2 = 1
(8) 2 = 64
sum them up = 106
N = 6
Variance =106/ = 17.67
Xbar = 8
Std Deviation =√ = 4.20

24. Now let’s try another on the promethean board 3, 4, 4, 8, 11

25. You try….. 2, 4, 5, 6, 8

26. Find the mean, range, variance and std. deviation of the following
2, 5, 6, 6, 7
9, 7, 6, 2, 3
1, 1, 5, 6, 7
8, 5, 6, 7, 3
4, 8, 1, 0, 3
Identify the following:
Which data group has the largest mean, std. deviation, and range.

27. 2, 6, 6, 7, 8, 9, 9, 9, 16
Frequency 1 2 3 X 2 6 7 8 9 16
(x-xbar) -6 -2 -1 1 8
(x-xbar)2
(-6) 2 = 36
(-2) 2 = 4
(-1) 2 = 1
(0) 2 = 0
(1) 2 = 1
(8) 2 = 64
(Freq)(x-xbar)2
(1)36 = 36
(2)4 = 8
(1)1 = 1
(1)0 = 0
(3)1 = 3
(1)64 = 64
sum them up = 112
N = 9
Variance =112/ = 12.44
Xbar = 8
Std Deviation =√ = 3.53

28. Show all of your work for standard deviation or no credit
Homework
Page 261 #13-17
Show all of your work for standard deviation or no credit