QBM117 Business Statistics Probability Conditional Probability.
Unit 4 – Probability and Statistics
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Transcript of Unit 4 – 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 GraphsGoal: 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 GroupsMeasures 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 Number of Terms
=44513
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
56 58 58 63 65 71 74 78 82 84 85 86
Median of data set Q2 = 72.5
Median of lower half Q1 = 60.5 Median of upper half Q3 = 83
71 58 56 63 84 74 85 82 86 78 65 58
71 + 742
= 72.5
58 + 632
= 60.5 82 + 842
= 83
Box-and-Whisker Plot
70 8060
Q2Q1 Q3
MaximumMinimum
56
50 90
60.5 72.5 83 86
Outlier
56 64 73 59 98 65 59
1 Find the mean, median, and mode of this data set.
2 Is there an outlier in this set.
3 If there is an outlier, remove it from the set and recalculate the mean, median, and mode.
67.71, 64, 59YES; 98
62.67, 61.5, 59
OutlierRules 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.
Because: 22 < ½(58) 22 < 29
YES; 22
Measures of Dispersion (Variation)
Measure 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.
Measures of Variation
56 58 58 63 65 71 74 78 82 84 85 86
Median of data set Q2 = 72.5
Median of lower half Q1 = 60.5 Median of upper half Q3 = 83
1. What is the range for this data set?
2. What is the interquartile range for this data set?
30
22.5
How to find Standard Deviation
1. Find the mean of the data set.
2. Find the difference between each data value and the mean.
3. Square each difference.
4. Find the mean (average) of the squares.
5. 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 data set Q2 = 72.5
Median of lower half Q1 = 60.5 Median of upper half Q3 = 83
1. What is mean of this data set?
71.67
Standard Deviation Steps 2 & 3x 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.
Mean of the squares:1425.28
12
= 118.77
Step 5: Take square root of the mean of squares.
Sigma σ = sqrt(118.77)
σ = 10.9
10.9 is our Standard Deviation
HOMEWORK
P. 449
#4 – 7 ALL
#11 – 27 ODD