1. Unit 4 – Probability and Statistics
Section 7.7
Day 9

2. Warm-Up
P. 982 #5 - 12

3. Warm-Up Review
5) About ) About ) About ) About ) 0.5
10) About ) About ) About 0.145

4. Section 7.7 Statistics and Statistical Graphs
Goal: Use measures of Central Tendency and Measures of Dispersion to describe data sets, and use box-and whisker plots to describe data graphically.
Statistics – numerical values used to summarize and compare sets of data
2 Main Groups
Measures of Central Tendency
Measures of Dispersion (Variation)

5. Section 7.7 Statistics and Statistical Graphs
MEASURES OF CENTRAL TENDENCY
Mean – the sum of data values divided by the number of data values is a mean (average).
Median – is the middle value of a data set. If the data set contains a even number of values, the median is the mean of the two middle numbers
Mode – The most frequently occurring value in a set of data.

6. Example 1 Find the mean, median, and mode for the given data set.
36, 39, 40, 34, 48, 33, 25,
30, 37, 17, 42, 40, 24
Mean:
Sum of the Terms
445 =
Number of Terms 13
Mean: 34.2

7. Example 1 (cont.)
Find the mean, median, and mode for the given data set.
36, 39, 40, 34, 48, 33, 25,
30, 37, 17, 42, 40, 24
Median:
Arrange terms from lowest to highest
17, 24, 25, 30, 33, 34, 36, 37, 39, 40, 40, 42, 48
Median: 36

8. Example 1 (cont.)
Find the mean, median, and mode for the given data set.
36, 39, 40, 34, 48, 33, 25,
30, 37, 17, 42, 40, 24
Mode:
Number that appears the most
17, 24, 25, 30, 33, 34, 36, 37, 39, 40, 40, 42, 48
Mode: 40

9. Section 7.7 Statistics and Statistical Graphs
Box-and-Whisker Plot – a box and whisker plot uses quartiles to form the center box and whiskers.
Quartiles – separate a finite data set into four equal parts.
Outlier – is an item of data with a substantially different value from the rest of the items in the data set.

10. Quartiles
Median of lower half Q1 = 60.5
Median of upper half Q3 = 83
= 60.5
= 83 2 2
Median of data set Q2 = 72.5
= 72.5 2

11. Box-and-Whisker Plot Q1 Q2 Q3 Maximum Minimum 56 60.5 72.5 83 86 50 6070 80 90

12. Outlier
Find the mean, median, and mode of this data set.
Is there an outlier in this set.
If there is an outlier, remove it from the set and recalculate the mean, median, and mode.
67.71, 64, 59
YES; 98
62.67, 61.5, 59

13. Outlier Rules for outliers: Maximum > 1.5(Median)
Minimum < ½(Median)
Given the data set:
Is there an outlier in this set.
YES; 22
Because: 22 < ½(58) < 29

14. Measures of Dispersion (Variation)
Definition
Range
Greatest Value – Least Value
Interquartile Range
Q3 – Q1
Standard Deviation
Measure of how each data value in the set varies from the mean.

15. Measures of Variation
Median of lower half Q1 = 60.5
Median of upper half Q3 = 83
Median of data set Q2 = 72.5
What is the range for this data set?
What is the interquartile range for this data set? 30
22.5

16. How to find Standard Deviation
Find the mean of the data set.
Find the difference between each data value and the mean.
Square each difference.
Find the mean (average) of the squares.
Take the square root of the average. That is the standard deviation.

17. Data Set
Median of lower half Q1 = 60.5
Median of upper half Q3 = 83
Median of data set Q2 = 72.5
What is mean of this data set?
71.67

18. Standard Deviation Steps 2 & 3x
Mean
Difference
Squared Value 56
71.67
-15.67
245.55 58
-13.67
186.87 63
-8.67
74.17 65
-6.67
44.49 71
-0.67
0.45 74
2.33
5.43 78
6.33
40.07 82
10.33
106.71 84
12.33
152.03 85
13.33
177.69 86
14.33
205.35
SUM:

19. 10.9 is our Standard Deviation
Step 4: Find the mean of the squares.
Mean of the squares: 12 =
Step 5: Take square root of the mean of squares.
Sigma σ
= sqrt(118.77)
= 10.9
10.9 is our Standard Deviation

20. HOMEWORK
P. 449
#4 – 7 ALL
#11 – 27 ODD