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Math I
Unit 2: One-Variable Data
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Review Sheet
Up to Level 1 = you’ve got the basics….Up to Level 2 = you on your way… Up to Level 3 = Complete mastery – you are ready for the test!
Standard 1: S-ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).
Use the following data below for questions #1 – 3: Students in a Math 1 class were asked how many minutes they spend doing homework. Here are the results:
42 0
15 60 30 45 48 5 26 65 50 56 20 90 38 30 49 58
Level 1:
1.) a. Fill in the frequency table using
the data above.
Level 2:
2.) a. Create a histogram from the frequency table you
created in #1.
55
75
45 44
37 72
65
Level 3:
3.) a. Find the 5-number summary:
_____ ______ ______ ______ ______
Minutes
0 - 19
20 – 39
40 – 59
60 – 79
80 – 99
Frequency
b. What percentage of ratings are less
than 40?
b. Are there any outliers? Calculate the
boundaries using the 1.5(IQR) rule.
b. Describe the shape of the graph:
c.
Create a box plot using the information above.
Standard 2: S-ID.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard
deviation) of two or more different data sets.
Level 1:
4.) John and Laura babysit to earn extra money. The
amount of money (in dollars) that each has made for
each of the past 10 weeks is show below.
Level 2:
5.) On last week’s math test, Ms. Kinkaid and Ms. Schmucker gathered statistics on
their class. The results are below
Ms. Kinkaid: x = 84 and sx = 9
Ms. Schmucker: x = 79 and sx = 3
Which class was more consistent with their test scores? How do you know?
Level 3:
6.) Below are box plots representing quality rating values of natural and regular
peanut butters:
a. Without doing the actual computation, identify
which set will have a greater standard deviation.
Explain your reasoning.
b. Without doing the actual computation, identify
which set will have the greater mean. Explain
your reasoning.
a. Which peanut butter has the lowest rating? ___________________
b. Compare the measures of center.
c. Compare the measures of spread.
d. Make a convincing argument that natural peanut butter is better.
Standard 3: S-ID.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points
(outliers).
Level 1:
7.) Matching. Draw lines connecting the measure of center descriptions in the first column to a graph shape in the second column. Then match the situations in
the third column to an appropriate graph in the second column.
Measure of center
Graph shape
Statistic situation
Mean is less than the median.
d. Symmetric
g. The weight of babies born in the U.S.
b. Mean is greater than the median.
e. Skewed left
h. Age of deaths in the U.S.
c. Mean and median are about the same
f. Skewed right
i. A difficult test (many students did not do well)
a.
Level 2:
8.) Multiple Choice
Level 3:
9.) Jack looked at all his test scores for his class in a semester: 55, 98, 88, 85, 93, 77, 94
a. If you were to graph his test scores, describe the shape of the graph:
b. Jake decided to retake the 55% test grade and earned a 76%. If you changed his 55% to a
76% in the gradebook, which of the following would change? Circle all that apply.
Mean
Median
Range
Interquartile Range
Standard Deviation
c. State how the above circled would change – What would increase? What would decrease?
Answer Key:
1. a.
Minutes
0 - 19
20 – 39
40 – 59
60 – 79
80 – 99
b. 9/25 = 36%
2.
b. The shape is symmetric.
Frequency
3
6
10
5
1
3. a. 0, 30, 45, 59, 90
b. 30 – 1.5(29) = -13.5 and 59 + 1.5(29) = 102.5  there are no data values outside of -13.5 and 102.5, so no outliers
c.
4. a. Laura has greater standard deviation because her data is more spread out.
b. Laura has a greater mean because her she has a higher value (outlier of 55) which will increase the average.
5.
Since Ms. Schmucker has a smaller standard deviation of 3, this means her class has smaller spread; hence, her class is more consistent.
6. a. Regular pb
b. Natural pb has a higher median of 65 than regular pb with a median of 40.
c. Natural pb has a smaller spread even with the outliers (ranging from 30 to 90), where regular pb has a range over 70 (from about 10 to 80). In
addition, the IQR (the box) is smaller with natural pb.
d. Answers will vary, but here is an example: Natural peanut butter is best because it has the highest ratings, the highest median, and its ratings
are more consistent (lower spread) between the two.
7. a  f  h;
b  e  i;
9. a. skewed left
cdg
b. all circled except median
8.
D.
c. Mean – increase; Spread (range, IQR and Standard Deviation) – decrease