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104 CHAPTER 2 • Modeling One-Variable Quantitative Data

Suppose we convert the passage time measure- 30
LESSON APP 2.2 Answers ments to nanoseconds by adding 24,800 to each 25
data value.
1. The shape would remain the same: 1. What shape would the resulting distribution have? 20

fairly symmetric and single-peaked with 2. Find the median of the distribution in nanoseconds. Frequency 15

two low outliers. 3. Find the interquartile range ( IQR ) of the distribution 10

+
=
=
2. Median 27 24,800 24,827 in nanoseconds. 5
nanoseconds After performing the transformation to nanoseconds,
we could convert the measurements from nanoseconds 0
0
15
–15
–45
–30
45
30
3. The IQR would remain the same: to seconds by dividing each value by 10 . Passage time (deviations from 24,800 nanoseconds)
9

IQR = 7nanoseconds. 4. Describe the shape, center (median), and variability n Mean SD Max

Min Q 1
4. The shape would remain the ( IQR ) of this distribution. 66 26.21 10.75 –44 24 Med Q 3 40
27
31
same and the measures of center and 5. Challenge: Use the information provided to estimate
(C) 2021 BFW Publishers -- for review purposes only.
9
variability would be divided by 10 . the speed of light in meters per second. Be prepared
Median = 24,827 ÷10 9 = 0.000024827 to explain the method you used.
7
secondand IQR =÷10 9 = 0.000000007
second. Lesson 2.2
=
5. Distance 7400meters. We will use
median = 0.000024827 second to estimate WHA T DID Y OU LEARN ?
time. LEARNING TARGET EXAMPLES EXERCISES
distance 7400 meters Describe the effect of adding or subtracting a constant on a p. 99 5–8
Speed = = distribution of quantitative data.
time 0.000024827 seconds
= 298,062,593.1m/s Describe the effect of multiplying or dividing by a constant on a p. 100 9–12
distribution of quantitative data.
Analyze the effect of adding or subtracting a constant and p. 102 13–16
multiplying or dividing by a constant on measures of center,
CHAPTER 2 ACTIVITY: location, and variability.
WHERE DO YOU STAND?
This optional activity can be used
any time after Lesson 2.2. Access it by Exercises Lesson 3.1
clicking on the link in the TE-book or by
logging into the teachers’ resources on Building Concepts and Skills Mastering Concepts and Skills
5.
our digital platform. 1. Give a possible reason for transforming data when pg 99 Step right up! A dotplot of the distribution of height
analyzing the distribution of a quantitative variable.
for Mrs. Nataro’s class is shown, along with some
numerical summaries of the data.
2. True/False: Adding a positive constant to each

FULL SOLUTIONS TO LESSON 2.2 value in a quantitative data set does not affect mea- d d d d d d d d d d d d d d d d d d d d d d d d d

sures of variability.
EXERCISES 3. If each value in a quantitative data set is divided by a 60 62 64 66 68 70 72 74
Height (in.)
You can find the full solutions for this positive constant, which characteristic(s) of the distri- Variable n − x s x Min Q 1 Med Q 3 Max
bution would not change: shape, center, or variability?
lesson by clicking on the link in the 4. If a distribution of quantitative data with mean 10 Height 25 67 4.29 60 63 66 70 75

TE-book or by logging into the teachers’ and standard deviation 2 is converted to z -scores, the
resources on our digital platform. new distribution would have mean Suppose that Mrs. Nataro has the entire class
and standard deviation . stand on a 6-inch-high platform and then asks the
Answers to Lesson 2.2 Exercises
1. To examine the data in different units
of measurement, for example, in feet
instead of inches. 03_StarnesSPA4e_24432_ch02_088_153.indd 104 07/09/20 1:54 PM
2. True
3. Shape
4. 0; 1

104 CHAPTER 2 • Modeling One-Variable Quantitative Data

03_TysonTEspa4e_25177_ch02_088_153_4pp.indd 104 10/11/20 7:44 PM