1. Organizing, Summarizing, &Describing Data UNIT SELF-TEST QUESTIONS
Statistics and Data Analysis
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Organizing, Summarizing, &Describing Data
Probability
Displaying Data
is about...
Family of Distributions
Center
Spread
Shape
Slope Triangles
Standard Deviation
5 Number Summary & Box Plot
Mean
Stem and Leaf Plot
Histogram
When is it better to use a histogram than a boxplot?
What does standard deviation tell you?
How are the boxplot and histogram limited in what they can tell you about the data?
How do outliers influence the mean?
What does the spread tell you about the data?
Why can’t you make a histogram with categorical data?
When would you use a bar graph instead of a pie chart?
UNIT SELF-TEST QUESTIONS

3. Bill Gates makes $500 million a year
Bill Gates makes $500 million a year. He’s in a room with 9 teachers, 4 of whom make $40k, 3 make $45k, and 2 make $55k a year. What is the mean salary of everyone in the room? What would be the mean salary if Gates wasn’t included?
Mean With Gates:
$50,040,500
Mean Without Gates:
$45,000

4. How do we determine if a number is an outlier?
To find any outliers in a set of data, we need to find the 5 Number Summary of the data.

5. 5 number summary and boxplots A five number summary is a statistical tool used to quickly summarize and gain insight about a set of data.
A boxplot provides an alternative to a histogram, a dotplot, and a stem-and-leaf plot. Among the advantages of a boxplot over a histogram are ease of construction and convenient handling of outliers. In addition, the construction of a boxplot does not involve subjective judgements, as does a histogram. That is, two individuals will construct the same boxplot for a given set of data - which is not necessarily true of a histogram, because the number of classes and the class endpoints must be chosen. On the other hand, the boxplot lacks the details the histogram provides.
Dotplots and stemplots retain the identity of the individual observations; a boxplot does not. Many sets of data are more suitable for display as boxplots than as a stemplot. A boxplot as well as a stemplot are useful for making side-by-side comparisons.

6. Constructing a box and whisker plot
Step 1 - Find the median: the middle value in a data set when you put the numbers in order.
18, 40, 50, 58, 59, 59, 61, 68, 69, 70, 70, 71, 80, 93, 100
68 is the median of this data set.

7. Step 2 Find the lower quartile.
The lower quartile is the middle of the data set to the left of median.
(18, 40, 50, 58, 59, 59, 61), 68, 69, 70, 70, 71, 80, 93, 100
58 is the lower quartile

8. Step 3 Find the upper quartile.
The upper quartile is the middle of the data set to the right of the median.
18, 40, 50, 58, 59, 59, 61, 68, (69, 70, 70, 71, 80, 93, 100)
71 is the upper quartile

9. 18 is the minimum and 100 is the maximum.
Step 4
Find the maximum and minimum values in the set.
The maximum is the greatest value in the data set.
The minimum is the least value in the data set.
18, 40, 50, 58, 59, 59, 61, 68, 69, 70, 70, 71, 80, 93, 100
18 is the minimum and 100 is the maximum.

10. Find the Interquartile Range (IQR)
Step 5
Find the Interquartile Range (IQR)
18, 40, 50, 58, 59, 59, 61, 68, 69, 70, 70, 71, 80, 93, 100
= 19.5

11. Step 6 Mark the upper and lower fence
 lower fence (LF):  Q1 – 1.5×IQR  
Upper fence (UF):  Q3 + 1.5×IQR
If LF and UF is within data set mark boundaries and Dot in outliers (otherwise keep max min marks)
18, 40, 50, 58, 59, 59, 61, 68, 69, 70, 70, 71, 80, 93, 100
30.5
90.5

12. Example
The weights of 20 randomly selected juniors are recorded below:
a) Construct a boxplot of the data
b) Determine if there are any mild or extreme outliers.
121
126
130
132
143
137
141
144
148
205
125
128
131
133
135
139
147
153
213

13. Example - Answer
Q1 = median = 138 Q3 = Min = 121 Max = 213 IQR = 15 UF = 168 LF = 108 * *
Weight

14. Quick Write: Compare these two boxplots

15. Distribution Shape Based on Boxplots:
If the median is at the center of the box and each horizontal line the data is symmetric
(mean is equal to the median)
median is to the left of the center then data is skewed right
(mean is right of median)
median is to the right of the center then data is skewed left (mean is left of median)

16. Page 89 #3, 8 a&b only, 19, 21