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LESSON 2.2 • Transforming Data 105

5. (a) The same shape: slightly
students to measure the distance from the top of 9 Taller by the inch Refer to Exercise 5 Suppose that
.
.

their heads to the ground. pg 100 you convert the class’s heights from inches to centi- skewed right with several

(a) What shape would this distribution of distance meters (1 in. = 2.54cm) . peaks. (b) Mean: 67 +=673in.;
have? (a) What shape would the resulting distribution of median:666

+= 72in. (c) SD: 4.29 in.;

(b) Find the mean and median of the distribution of height have? Explain your answer.

distance. (b) Find the mean of the distribution of height in IQR: 7 in. Lesson 2.2
(c) Find the standard deviation and interquartile range centimeters. 6. (a) The same shape: fairly symmetric

(IQR) of the distribution of distance. (c) Find the standard deviation of the distribution of

height in centimeters. with several peaks. (b) Mean:577.3–20 =
6. Long jump There were 40 athletes competing in the

long jump at a major track meet. The meet official 10. Jump up! Refer to Exercise 6 Suppose that the 557.3cm; median: 577–20 = 557 cm

.
recorded the distance, to the nearest centimeter, of corrected long-jump distances are converted from (c) SD: 4.713 cm; IQR: 7 cm

each athlete’s best jump. Here are a dotplot and centimeters to meters (note that 100 cm = 1m ).
some numerical summaries of the data. (a) What shape would the resulting distribution have? 7. (a) The shape will be the same. (b) The

Explain your answer. mean and median will each be $1000
5review purposes only.

(b) Find the mean of the distribution of corrected long-
jump distance in meters. greater. (c) The standard deviation and

565 570 575 580 585 (c) Find the standard deviation of the distribution of IQR will each be the same.
Long-jump distance (cm) corrected long-jump distance in meters. 8. (a) The shape will be the same. (b) The

11. Making more money Refer to Exercise 7 . Suppose each
n Mean SD Min Q 1 Med Q 3 Max teacher receives a 5% raise instead of a $1000 raise. mean and median will each be $500 less.
40 577.3 4.713 564574.5 577 581.5 586 What effect will this raise have on each of the following (c) The standard deviation and IQR will

characteristics of the resulting distribution of salary?
The meet official realized that he measured (a) Shape each be the same.

all the jumps from the back of the board instead of

the front. Thus, he had to subtract 20 centimeters (b) Median 9. (a) The shape will be the same:

from each jump to get the correct measurement. (c) Interquartile range slightly skewed right with several peaks.
(a) What shape would the distribution of corrected 12. Used cars, cheaper! Refer to Exercise 8 . Suppose each (b) Mean 67 2.54 170.18 cm

×
=
=
long-jump distance have? car’s price is reduced by 10% instead of by $500. What
=
×
=

(b) Find the mean and median of the distribution of effect will this discount have on each of the following (c) SD 4.29 2.54 10.90 cm
corrected long-jump distance. characteristics of the resulting distribution of price? 10. (a) The shape will be the same:

bution of corrected long-jump distance. (b) Mean fairly symmetric with several peaks.
=
×

7. Teacher raises A school system employs teachers at (c) Standard deviation (b) Mean: 577.30.015.773m

=
salaries between $38,000 and $70,000. The teach- 13 Cool pool? Coach Ferguson uses a thermometer to (c) SD :4.713 × 0.01 0.04713m

.
ers’ union and school board are negotiating the pg 102 measure the temperature (in degrees Fahrenheit) at 20
form of next year’s increase in the salary schedule. different locations in the school swimming pool. An 11. (a) The shape will be the same.
(C) 2021 BFW Publishers -- for
Suppose that every teacher is given a $1000 raise. analysis of the data yields a median of 77 F° and an (b) The median will be 1.05 times the

What effect will this raise have on each of the fol-
lowing characteristics of the resulting distribution interquartile range of 5F° Recall that ° =C (F . median of the original salary distribution.
.

° − 32)
of salary? 9 (c) The IQR will be 1.05 times the IQR of

(a) Shape (a) Find the median temperature reading in degrees

Celsius.

(b) Mean and median (b) Calculate the interquartile range of the temperature the original salary distribution.

8. Used cars, cheap! A used-car salesman has 28 14. Measure up Clarence measures the diameter of each shape of the original price distribution.
cars in his inventory, with prices ranging from tennis ball in a bag with a standard ruler. Unfortu- (b) The mean will be 0.90 times the mean
$11,500 to $25,000. For a Labor Day sale, he nately, he uses the ruler incorrectly so that each of his
reduces the price of each car by $500. What effect measurements is 0.2 inch too large. Clarence’s data of the original price distribution. (c) The
will this reduction have on each of the following had a mean of 3.2 inches and standard deviation of standard deviation will be 0.90 times the
characteristics of the resulting distribution of 0.1 inch. Recall that 1 inch = 2.54 centimeters .
price? standard deviation of the original price

(a) Shape (a) Find the mean of the corrected measurements in distribution.

centimeters.
(b) Mean and median (b) Calculate the standard deviation of the corrected

5
(c) Standard deviation and interquartile range measurements in centimeters. 13. (a) Median = (7732) 25 °C

=
−
9
5
=
(b) IQR = (5)2.78C
°
9
=
14. (a) Mean (3.2 –0.2)2.547.62cm
=
×
03_StarnesSPA4e_24432_ch02_088_153.indd 105 07/09/20 1:55 PM
(b) SD 0.01 2.54 0.254 cm
×
=
=
LESSON 2.2 • Transforming Data 105
03_TysonTEspa4e_25177_ch02_088_153_4pp.indd 105 10/11/20 7:44 PM

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