Unit 5 – Data Representation –
Class Notes
Date
Statistical Questions
Learning Target: I will be able to identify statistical and non-statistical questions.
Key Terms
 Biased Question: Leads a person to a particular answer. You cannot draw valid conclusions
from biased data.
 Statistics: The process of collecting, organizing, and interpreting data.
 Statistical Question: A question that has many different, or variable, answers.
Examples/Try This
Statistical Questions…
Ashley asked her classmates, “How many miles do you travel to school?” The table below
shows the responses.
0.8 miles
2 miles
1 mile
Distances Traveled to School
1.5 miles
1.4 miles
0.75 miles
0.25 miles
0.5 miles
3 miles
1. Is there variability in the data?
2. Did Ashley ask a statistical question?
3. Explain why this is not a statistical question: “How many miles is the library from the
school?”
4. Is each question a statistical question? Explain.
a. How many siblings do you have?
b. In which month is your birthday?
c. What is your favorite type of book?
d. How many states are in the United States?
e. What color shirt am I wearing?
f. What is your favorite color?
g. How many dogs do you have?
h. What size shoe do you wear?
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Page 1
Biased Questions…
Dan and Kellie surveyed people about vacation spots. Dan asked, “Would you prefer to
vacation in sunny Bermuda or rainy London?” Kellie asked, “Would you prefer to vacation in
Bermuda or London?”
Survey Results
Dan
Kellie
Bermuda
Bermuda
London
London
Bermuda
London
Bermuda
London
Bermuda
Bermuda
Bermuda
Bermuda
Bermuda
Bermuda
London
Bermuda
1. How do Dan and Kellie’s answers differ?
2. What words did Dan use in his survey question that might influence the responses to his
question?
3. Is either question biased?
4. Complete the table.
Biased Question
Do you prefer exciting action
movies over boring drama
movies?
Do you prefer living in the
peaceful countryside or the
noisy city?
Do you want a delicious
chocolate cake or a bland
vanilla cake for your birthday?
Do you agree with most
people that playing the guitar
is cooler than playing the
clarinet?
Do you want to go for a tiring
run or play a fun game of
soccer?
Words Creating Biased
exciting, boring
Unbiased Question
What type of movie do you
prefer?
peaceful, noisy
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Page 2
Date
Measures of Central Tendency
Learning Targets
1) I will be able to calculate the mean, median, mode and range of a set of data.
2) I will be able to recognize outliers in a set of data.
Key Terms
 Measure of Center: A value that describes how data is centered. This includes mean, median,
and mode.
 Mean: This is sometimes called the average. To find this, add up all the values in the set and
divide by the number of items in the set.
 Median: This is the middle value when the data are in numerical order, from least to greatest.
If there are an odd number of items, it is the middle number; if there is an even number of
items, it is the mean of the two middle items.
 Mode: This is the value or values that appear the most often. There may be more than one
mode for a set of a data. If all values occur an equal number of times, then the data has no
mode.
 Outlier: This is a value in a set that is very different from the other values.
Examples/Try This:
1. Find the mean, median, mode and range for the following set of data:
5 30 35 20 5 25 20
2. The table shows the number of glasses of water consumed by several students in one day. Identify
the outlier in the data set. Then determine how the outlier affects the measures of central tendencies.
Water Consumption
Name
Randy
Lori
Anita
Jana
Sonya
Victor
Mark
Jorge
Glasses
4
12
3
1
4
7
5
4
3. Based on the following line plot, find the measures of central tendencies.
4. Twelve people estimated the time, in minutes, they spend reading each day. Their responses are as
follows: 20 5 45 90 60 45 30 10 30 45 15 25
Find the measures of central tendencies. Which one best describes the data?
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Page 3
Date
Measures of Variability
Learning Target:
1. I can find the Interquartile Range (IQR) and Mean Absolute Deviation (MAD) of a set of data.
Key Terms:
 Measure of Variability: A value that describes how data is spread out. This includes the range,
mean absolute deviation and interquartile range.
 Range: This is the difference in the least and greatest values in a set. To find this, take the
largest value minus the smallest.
 Interquartile Range (IQR): The difference of the upper quartile and the lower quartile.
 Mean Absolute Deviation (MAD): The mean distance between each data value and the mean
of the data set.
Examples/Try This:
Scientists recorded rainfall amounts in a rain forest for 10 days in June. The table below shows the
results.
June Rainfall
Day
1
2
3
4
5
6
7
8
9
10
Rainfall (cm)
5
6
8
16
7
6
1
5
9
7
1. One measure of variability is mean absolute deviation (MAD). The MAD is the average amount that
the data values vary from the mean.
Step 1 Find the mean value of the rain over the ten days.
Step 2 Complete the table below.
June Rainfall Distances from Mean
Day
1
2
3
4
5
6
7
8
9
10
Rainfall (cm)
5
6
8
16
7
6
1
5
9
7
Mean
Distance from Mean
Find the difference between each day’s rainfall and the mean to find the distance each day’s rainfall is
from the mean. Write each difference as a positive number.
Step 3 Calculate the mean of all the distances in the bottom row. This is the MAD, which is the
average amount that the data values vary from the mean.
2. Range is another measure of variability. What is the range of the rainfall data?
3. Another measure of variability is the interquartile range (IQR). This measure tells the spread of the
middle half of the data.
Step 1 Arrange the data values in order from least to greatest.
Step 2 Find the lower quartile and the upper quartile.
Step 3 Subtract the lower quartile from the upper quartile. This is the (IQR).
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Page 4
Date
Number Lines and Dot Plots (Line Plots)
Learning Targets: I am able to create and read information off of dot or line plots.
Key Terms
 Number Line: A line without ends whose points are matched to the real numbers by their
distance from a given point labeled zero.
 Dot Plot (Line Plot): A graph that shows the shape of a data set by stacking x’s above each value
on a number line. This is sometimes referred to as a line plot.
Examples/Try This
The line plot below shows the number of miles a cyclist traveled during a training period.
Cyclist A
x
x
x
x
x
x
x
x
x
x
x
x
x
x
2
3
4
5
6
7
8
9
1. In the plot for Cyclist A, the data are grouped around what value?
2. If you draw a vertical line at that value, are the points on either side symmetrical?
3. This line plot shows the distance traveled by another cyclist.
Cyclist A
x
x
2
x
3
x
4
x
5
x
6
x
x
x
7
x
x
x
x
8
x
9
a. Is there a value that the data are grouped around?
b. Are there more points to the left or the right of the graph?
4. Students in Mr. Gordon’s class ran several miles a week. The results are in the following
table. Organize the data into a dot plot.
Number of Miles Ran
3
4
5
6
7
8
9
10
Number of Students
5
0
6
4
3
7
0
2
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Page 5
Date
Histograms
Learning Target: I am able to create and read information off of histograms.
Key Terms
 Histogram: A type of bar graph that shows the frequency of data within given intervals. The
label under each bar tells the range of numbers the bar represents, and the height represents
the frequency. There is no space between the bars.
 Intervals: A set of numbers consisting of all the numbers between a pair of given numbers
along with either, both, or none of the endpoints.
Examples/Try This:
The histogram shows the scores for a test that was given in Mr. Warren’s English class.
Test scores in English Class
76 – 80
81 - 85
86 – 90
91 – 95
Test Scores
96 – 100
1. What does the bar labels 81-85 represent?
2. What values are included in the interval 91-95?
3. Compare all of the intervals shown on the horizontal axis of the histogram. Do any of the intervals
overlap or have a gap between them?
4. How many students are in the English class? Explain how you found your answer.
5. For each question below, answer the question or tell why the answer cannot be determined.
a. Which interval includes the most test scores?
b. How many students had a test score of 95?
c. How many students have test scores below 86?
d. How many students have test scores below 88?
e. What is the highest test score in the class?
6. Make a list of numbers that could represent the data graphed in this histogram.
7. The table below shows the number of minutes that Samuel spent on the computer each day for a
month. Use the data to complete the frequency table and make a histogram.
Samuel’s Computer Time
95
4
26
95
4
87
36
47
26
51
23
18
45
81
76
24
57
7
16
62
70
20
45
16
32
37
64
8
28
44
Sam’s Computer Time
Minutes Frequency
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Page 6
Date
Box Plot (Box-and-Whisker Plot)
Learning Targets
1) I will be able to read information from a box-and-whisker plot.
2) I will be able to create a box-and-whisker plot.
Key Terms
 Box-and-Whisker Plot: Shows how a set of data is distributed. The plot displays five numbers
that summarize the data.







Parts of Box-and-Whisker Plot
Lower Extreme (LE): the smallest value, that is not an outlier
Lower or 1st Quartile (LQ): the median of the lower half of data
Median: the middle value when placed in numerical order
Upper or 3rd Quartile (UQ): the median of the upper half of data
Upper Extreme (UE): the greatest value, that is not an outlier
Other Important Terms
Inter-quartile Range (IQR): upper quartile minus the lower quartile
Outlier: a value that is a lot bigger or smaller than the other values
 Mathematical formula for finding outliers
o Any number smaller than LQ - IQR(1.5)
o Any number bigger than UQ +IQR(1.5)
Steps to Making a Box-and-Whisker Plot
Make a box-and-whisker plot for the following set of data:
43, 42, 44, 46, 47, 42, 49, 47, 44, 47
1. Put the numbers in order from least to greatest.
2. Find the median of the set of numbers
3. Find the lower and upper quartiles. Remember, this is just the medians of the upper and lower
numbers.
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4. On an appropriate number line, draw a box extending from the lower quartile to the upper quartile.
Draw in the median using a dotted line. What do you think is meant by the word appropriate?
5. Fill in the “Whiskers” by connecting the lower extreme (excluding outliers) to the lower quartile and
the upper extreme (excluding outliers) to the upper quartile.
6. If you have any outliers, they are simply dots at the given values.
Five things you need to make a box-and-whisker plot
Lower Extreme:
Upper Extreme:
Lower Quartile:
Upper Quartile:
Median:
Try This
Draw a box-and-whisker plot for the following numbers.
45
43
61
64
51
35
55
37
66
59
58
49
50
47
62
Five things you need to make a box-and-whisker plot
Lower Extreme:
Upper Extreme:
Lower Quartile:
Upper Quartile:
Median:
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Page 9