Download Chapter 11 – More Probability and Statistics

Unit 4 – Probability
and Statistics
Section 7.7
Day 9
Warm-Up
P. 982 #5 - 12
Warm-Up Review
5) About 0.651
6) About 0.154
7) About 0.308
8) About 0.019
9) 0.5
10) About 0.265
11) About 0.505
12) About 0.145
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)
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.
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
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
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
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.

Quartiles
71 58 56 63 84 74 85 82 86 78 65 58
56 58 58 63 65 71 74 78 82 84 85 86
Median of lower half Q1 = 60.5
58 + 63 = 60.5
2
Median of upper half Q3 = 83
82 + 84 = 83
2
Median of data set Q2 = 72.5
71 + 74 = 72.5
2
Box-and-Whisker Plot
Q1
Q2
Q3
Maximum
Minimum
56
50
60.5
60
72.5
70
83 86
80
90
Outlier
1
2
3
56 64 73 59 98 65 59
Find the mean, median, and mode of this
data set. 67.71, 64, 59
Is there an outlier in this set. YES; 98
If there is an outlier, remove it from the
set and recalculate the mean, median,
and mode. 62.67, 61.5, 59
Outlier
Rules for outliers:
Maximum > 1.5(Median)
Minimum < ½(Median)
Given the data set:
22 40 42 45 50 58 64 73 65 65 83
Is there an outlier in this set. YES; 22
Because: 22 < ½(58)
22 < 29
Measures of Dispersion (Variation)
Measure
Definition
Range
Greatest Value – Least Value
Interquartile
Range
Standard
Deviation
Q3 – Q1
Measure of how each data value in
the set varies from the mean.
Measures of Variation
56 58 58 63 65 71 74 78 82 84 85 86
Median of lower half Q1 = 60.5
Median of upper half Q3 = 83
Median of data set Q2 = 72.5
1. What is the range for this data set? 30
2. What is the interquartile range for this
data set? 22.5
How to find Standard Deviation
1.
2.
3.
4.
5.
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.
Data Set
56 58 58 63 65 71 74 78 82 84 85 86
Median of lower half Q1 = 60.5
Median of upper half Q3 = 83
Median of data set Q2 = 72.5
1. What is mean of this data set?
71.67
Standard Deviation Steps 2 & 3
x
Mean
Difference
Squared Value
56
71.67
-15.67
245.55
58
71.67
-13.67
186.87
58
71.67
-13.67
186.87
63
71.67
-8.67
74.17
65
71.67
-6.67
44.49
71
71.67
-0.67
0.45
74
71.67
2.33
5.43
78
71.67
6.33
40.07
82
71.67
10.33
106.71
84
71.67
12.33
152.03
85
71.67
13.33
177.69
86
71.67
14.33
205.35
SUM:
1425.28
Standard Deviation
Step 4: Find the mean of the squares.
1425.28
Mean of the squares:
12
= 118.77
Step 5: Take square root of the mean of
squares.
Sigma
= sqrt(118.77)
σ
σ
= 10.9
10.9 is our Standard Deviation
HOMEWORK
P. 449
#4 – 7 ALL
#11 – 27 ODD