1. Warm Up
Find the mean, median, mode, range, and outliers of the following data.
11, 7, 2, 7, 6, 12, 9, 10, 8, 6, 4, 8, 8, 7, 4, 7, 8, 8, 6, 5, 9
How does an outlier affect the data set?
Draw an example of a histogram that is skewed, and draw an example of one that is symmetrical.
Of 35 judges’ scores awarded during a gymnastics meet, 28 are less than or equal to 7.5. What is the percentile rank of a score of 7.5?

2. Box and Whisker Diagrams.
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140
150
160
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190
Boys
Girls cm
Box and Whisker Diagrams.
Box plots are useful for comparing two or more sets of data like that shown below for heights of boys and girls in a class.
Anatomy of a Box and Whisker Diagram.
Lowest Value
Lower Quartile
Upper Quartile
Highest Value
Median
Whisker
Box 4 5 6 7 8 9 10 11 12
Box Plots

3. 2. The boys are taller on average.
Question: Gemma recorded the heights in cm of girls in the same class and constructed a box plot from the data. The box plots for both boys and girls are shown below. Use the box plots to choose some correct statements comparing heights of boys and girls in the class. Justify your answers.
Drawing a Box Plot.
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Boys
Girls cm
1. The girls are taller on average.
3. The girls show less variability in height.
4. The boys show less variability in height.
5. The smallest person is a girl.
6. The tallest person is a boy.

4. Comparing Box and Whisker Plot
We can see that in general the scores in the first approval poll are lower and not as wide spread as those of the second approval poll. 1 2 3 4 5 6 7 8
Approval Poll One
Approval Poll Two

5. Which has the highest death rate?
How many years of smoking has the least amount of variability?
Which one has the smallest median?

6. Which type of house has a higher average cost?
Which house has the highest price?
Which house has the lowest price?
Which has the highest median?
Which type has a larger spread, or variability in pricing?

7. STANDARD DEVIATION

8. Depart from what’s normal
Standard Deviation: tells us how far, on average, our data points are from the mean.
EX: Given the following data set: 2, 4, 4, 4, 5, 5, 7, 9
The mean is 5, and the standard deviation is 2. That means that on average, the data points are 2 units away from the mean of 5.

9. Calculate Standard Deviation

10. Calculate Standard Deviation
Luckily, we can also find it in our calculator by:
Going to STAT then Edit
Typing our data set into L1
Pressing STAT then CALC and 1-Var Stats
You will see a lot of numbers. The standard deviation looks like this: σx =
**If it is a number with a lot of decimals, you can round to the hundredths place (2 digits after the decimal)

11. Other Fun Things From the Calc.
x= minX=
∑x= maxX=
n = Med=

12. Examples:
Find the standard deviation of: , 19.4, -33.1, -6.4, -8.2, 2.9, 4.3, -21, 1.7, and -21

13. Examples (cont.): Find the standard deviation of:

14. Using Standard Deviation
If you are given mean and standard deviation and told to find a particular value...
Start with the mean
Add or subtract the standard deviation from the mean until you get what you need.

15. Using Standard Deviation
Mrs. Inscoe graded all of the Algebra I quizzes and found that they had a mean of 80 and a standard deviation of 4. She tells you that you earned a score of 1 standard deviation above the mean, but that another student earned a score 1 standard deviation below the mean. What are your two scores?

16. Using Standard Deviation
You look up your favorite basketball player’s scoring average and find that his mean points scored per game is 22 and his standard deviation is 6. If he scored 2 standard deviations below the mean in his game against the Bobcats, how many points did he score in that game? What about if he had scored 1 standard deviation above the mean?

17. Using Standard Deviation
Drivers in Charlotte commute on average 8 miles to get to work, with a standard deviation of 2 miles. If you have to commute 3 standard deviations above the mean, how far do you have to go to commute to work?

18. Shapes of Data Uniform- roughly the same height throughout
Symmetric- you could draw a vertical line that divides the graph into two parts that are close to mirror images
Skewed- 1 peak, not in the center (left, and right)

19. Even More Vocabulary
Cumulative Frequency Table- a frequency table that has an additional column that calculates a total for the data at each interval

20. Height Data Height Interval Frequency Cumulative Frequency 4’7” – 5’
5’1” – 5’6”
5’7” – 6’
6’1” – 6’6”

21. You Try!
Complete the Frequency Table

22. Still More Vocabulary
Histogram - a graph that shows data from a frequency table
Height shows frequency of the interval
No gaps between bars
Bars have equal widths

23. Height Data

24. Box & Whisker Plots
Q1 is the lower quartile & represents the values in the lower 4th (bottom 25%) of the data
Q3 is the upper quartile & represents the values in the upper 4th (top 25%) of the data
Q2 is the median
The box from Q1 to Q3 is the middle 50% of the data known as the interquartile range

25. Five Number Summary
Min value Q1 Q2 Q3 Max Value

26. Box & Whisker Plots
Describe the data represented by the box and whisker plot. Include the extreme values and quartiles. 1. 2.

27. Examples
Find the minimum, first quartile, median, third quartile, and maximum of each data set.
18, 14, 15.8, 9, 12, 16, 20, 16, 13, 15
125, 80, 140, 135, 126, 140, 350, 75

28. Outliers
If the data set has outliers, they are represented by bullets, do not include them in the whiskers.
Remember these outliers skew the mean and standard deviation!
Outlier is any element of a set of data that is at least 1.5 interquartile ranges less than the lower quartile (Q1) or greater than the upper quartile (Q3)
Q1 – 1.5IQR Q IQR

29. Outliers Example: Identify any outliers.
12, 12, 17, 23, 23, 23, 24, 24, 25, 26, 26, 28, 28, 29, 30, 31, 34, 36, 40, 46

30. Making a Box & Whisker Plot
Daily attendance: 29, 24, 28, 32, 30, 31, 26, 33, 14
In the calculator, enter data in L1 and choose the box and whisker icon in the StatPlot menu.

31. Box & Whisker Plot Shapes

32. Percentiles
Percentiles separate data sets into 100 equal parts. The percentile rank of a data value is the percentage of data values that are less than or equal to that value.
Examples: Of 25 test scores, eight are less than or equal to 75 and seven scores are between 75 and 85.
What is the percentile rank of a test score of 75?
What is the percentile rank of a test score of 85?

33. Examples (cont.)
Of 10 bowling scores, six are less than or equal to What is the percentile rank of a bowling score of 120?
Of 35 judges’ scores awarded during a gymnastics meet, 28 are less than or equal to 7.5. What is the percentile rank of a score of 7.5?