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Unit l - Exploring One Variable Data
Unit 1 Test Review
-1 wtirw""
Name: _ K___;;e;._a.~----
C l) Nctflix gathers a lot of data on user activity when streaming a movie. The following is a description of five variables that are gathered. .
I. The genre of the movie being watched C
Il. The time spent watching the movie Q m. The age of the account holder who is watching the movicQ N. The name of the movie C,
V. The number of times the account holder watches the movie Q
Which of the following is a true statement?
(A) D, llI, and V arc categorical and the rest are quantitative @ I, N, and V are categorical and the rest are quantitative B I and N are categorical and the rest are quantitative (D) m and V are categorical and the rest are quantitative (E) II and N are categorical and the rest are quantitative
A 2) The following histogram shows the ages of kids at the local daycare.
Which of the following statements arc TRUE?
1. The mean age is greater than the median age.T II. The median age is greater than the mean age. I=
m. The range is 7 years. F ~ G, \ b ➔~~
■ I only
(B)Donly
(C)IDonly
(D) I and II
(E)Ilandill
ran8~
R,-9\\+S~ol
l\'\e. c1·.an le. O.f'e ..\-o\d a·.~ 5',lt\~t.-lrk. I So -fr 9 5 7
Which of the following are true? 9 10 0 8
i"" I. The third quartile of Comedy is equal to the first quartile of Action ~= , SS
-rn. The IQR of Action is larger than the IQR of Comedy M DO( 'I I~ 3
-rm. The range of Action is larger than the range of Comedy XQR, YO
5 3 11 5
{A) II and m only
{B) II only
{C)IDonly
12 4
4 2 13 4
3 14
R f:U,\tlt c S'i 7 5 .., 0 15
3 16
t"'fn ~ i4
Q,~s'\
Q3~ns
'""°'"~ 13'-I
I.G?R:. 2b
Rc.tage ~ so
@ I and II only
■ I, II, and m are all correct
Length of Movie
KEY: 1613 = 163
Use the following situation to answer questions 7 - 9:
In college baseball, the speed a pitcher throws a curveball is normally distributed with a mean of 87 mph and a
standard deviation of 4.5 mph.
B ~ ~I'\. d.e"
__ 7) According to the Empirical Rule, the middle 95% of college pitchers who throw a curveball throw
between which two speeds?
~ 82.5 mph and 91.5 mph
llll 78 mph and 96 mph
{C) 82.5 mph and 96 mph
{D) 78 mph and 100.5 mph
(E) 87 mph and 100.5 mph
'81 ± a ('-f. s) =
18
A- 8) What percentage of pitchers can throw above a curveball above 9S mph?
■3.77%
(B) 13.45%
{C)8.25%
{D) 1.83%
(E) 96.23%
P(x ~ 95) _
L U. X Sx
Y)orma\cd+( q5> le.'tq., i,, LJ.s) = o.os,7
G 9) Suppose that major league scouts will only consider pitching prospects who can throw a curveball.!t.
least 90 mph. What percentage $,_theJ?,itching f:?Spects w~~ consid~, can __ thro_ w_a_t.,:speeds __ ov_er_ 9_5_mp __ h_?
{A) 6.690/4
@.25.25%
IIJ 14.94%
(0)45.22%
(E) 3.77%
% 4-~row over qSmph _ oor,n 145 1'0 US
~c Blood Pressure(~
_E....;__ 10) Which of the following best describes the first quartile, median, and third quartile?
(A) Q1 = 105, Med= 110, Q3 = 118
(B) Q1 = 111, Med= 115, Q3 = 124
(C) Qi= 108, Med= 120, 03 = 145
ill) Qi = 95, Med = 124, Q3 = 155
II Qi = 118, Med= 124, Q3 = 135
~ 11) Which of the following histograms best displays the data above?
(A)
24.0% ID
~ 2'.0%
~
I - J 20.°'6
16.0%
14-0,i
I 1%.0% j 15.0M,
10-
t.0% lo.oti
6.11% ·- "°" 2-
O.o!6
IIO ----------100 110 llO ut 1-10 uo 160 .,.. ... _
~~p
-ro l55
(C) 24.0%
no,i,
20.0%
l
IU%
US.Cl%
14.CM
j 110%
10.0%
a.o,i,
0.
VC-.\~.s lt.SS
~\\~Y\ 10$
(E) S5a
l°'°"
(D)
I
I
---1 ''° n -the ojlve, ?o is acOAMIAlcnftl
~~- so~"~ \S ~o. be..~
~ ~ \l()(ueS
E 12) At the Majestic Oaks golf course, the par for 18 holes is a score of 70. Ronnie and his friends love
golfing the comse and they have compiled their scores for this past summer. From a total of 20 scores, here are
the following summary statistics:
x Median Mode Min Max
75.5 75 75 6.37 70 78.5 65 89
Which of the following statement( s) are correct?
I. 25% of scores were below 70. lt""e., Q, =,O
II. This distribution is approximat.ely symmetric. I"\~"~ l"\eflioW\ S6 -true. \ .. , ' . ~(. o-m. According to the 1.~ x IQR rule, there are no outliers. :cQ~ = i -~ rt\0.-'1 '~o~~,f(S
TrCAe... ,s-~.., ,.e;,(1.~ ';'. t:t1:~5 ✓ e:.~ t\O
WI~ .
(B) I and II only
(C)illonly
(D) I and m only
fl) 1, II, and m
L 13) A recent Pew poll asked a random sample of teenagers the following question: "Do you believe the
current US president is doing a good job?". 45% of males responded '"{es" and 67% of females responded
"Yes". What does this infonnation tell you about the shape of the distirbution?
(A) The distribution is bimodal. C o\-e y~\ca.\ dis-4r~bu.\ior'\ ~
(B) The distirbution is symmetric around 56% ~() re.\- \\ove. Q. ~ha~~
(C) The distirbution is skewed towards males.
ill) The distirbution is skewed towards females.
II This is categorical data, so we cannot determine the shape of the distribution.
G 14) If the standard deviation of a set of data is zero, we can conclude that
(A) there is no relationship between the x values
@ the mean is 0 a all observations are the same value
(D) all observations are different
(E) the median is 0
C 15) A population distribution is approximately normal with a mean of 45 and a standard deviation of
3.5. Let x be a randomly selected member of the population. Which of the following statements is (are) correct?
1 P(39 47) = 0.2839 "Trv.e.
(A) I, 14 and II
{fil I and Il only
II n and m only
(D) I and m only
(E)Ilonly
'B 16) A student obtained a ~re of -1.40 on a national test for which the mean score was 500 and the
standard deviation was 50. The student's actual test score was
®570
. 430
(C) 564
(D) 640
(E)450
-\.L\O=- X-500
so
--,o = x-Soo
430 =-.X
D 17) The ages of all US presidents at their first inauguration are approximately normally distn'buted, with
a standard deviation of7.27 years. George Washington was 57 years old when he took office and this placed
him at the 58th percentile. Which of the following is the closest approximation of the mean age of all US
presidents?
(A) 50.1
(B) 52.3
(C) 53.1
. 55.5
(E) 59.5
·,V'\\J~or't"(.s~=- 2 ~ o . ~C>a ~ 57-x
7:a,
I . 4 7 :. 57 - 'i:
-X =- 5':) •. 53
D 18) A teacher is teaching two AP Statistics classes. On the Unit 1 test, the 25 students in the first class
average a score of 87, while the 15 students in the second class averagea score of 92. If the teacher combines
the classes, what will the average Unit 1 test score of all her students?
°'87-::.. L_X I
~5
9'd.:. z:x ..
,s
1-011~131)
40
~:. ii-~
(A) 89.5
(B) 91.2
.{9_ 87.9
llJ 88.9
(E) 90.4 ~~& d-175 LX;a. ~ 1'380
Use the following information to answer questions 19 and 20:
The following graph shows the list prices of 33 homes currently on the market in an aftlent area in the state. The
prices are listed in thousands of dollars.
t>
i
10 t r::
8
6
4
2
0
0 500 1000 1500 2000 2500 3000 3500 4000
8-Prtcies(lll .... , ... sorW■n)
(., 19) Based on the histogram, which of the following statements must be true?
= \(o. 5
~ .
r\ed-io-n 15
b~-twt~"~
\(o s. \l '1 o. ,~e
·"~c:,~~
' \;SY
(A) The minimum price is $0 • .. b/ ,I, 0 ncJ.. SOO ()00
@The maximum price is $4,000,000 _ ./ tvted,O.I\ 1 ~ °' '
81 Theroedianpriceisnotgreaterthan$1,000,000V .. ~ SRewetl so mc:An is 9~..\or
(D) The mean price is between $0 and $500,000 ~ "'S ~ -\~e, 1V'C,clklY\..
(E) The upper quartile of the prices is greater than $1,500,000 ~ 1\.
f-) 20) The standard deviation in the problem above is $788,417. Which of the following is the best
description of the standard deviation?
• The approximate mean distance between the listed home price and the mean home price.
(B) The approximate median distance between the listed home price and the mean home price.
(C) The distance between the greatest listed home price and the mean home price
(D) The amount of money separating the smallest home price and the largest home price when considering all
home prices in the area.
(E) The amount of money separating the smallest home price and the largest home price when considering the
middle 50% of the distribution of all home prices in the area.
I) Below are the fuel efficiencies (in mpg) of small cars vs sporty cars on the marlcet in 2020.
Small Cars
50 45 37 37 37 36 35
34 34 34 34 33 33 33
Sporty Cars
33 32 32 32 32 31 31
31 31 31 31 30 30 30
30 30 30 30 30 29 29
29 29 29 29 29 29
a) Create a graph that compares the two distributions. You can choose any graph that you feel describes this
data the best
f\ I •
I l \11\\\\\11 11 ll' \\\I l lllllt
'ft, 4.5 5o S':)
(t.t"lc',uc,e~ (Mp5)
b) Compare these two distributions. What do you notice?
&th di~rib«l . Srno.\\ cors 'no.~°'
h\~\\e,(" t(\t.O,nY\ o~ 35~p~ +~Q(\ spo~ co rs wni c.~ ha.S ~ rtlecl:°'"-
e + ~O ""'P~· S~°'\\ YI spoY~ cars
\'°:) LIWW'Pj w\\,\e. +\\~ ~°'l\8 ~ on C:SY\'\o \\ c.a-rs ·1.5 11 ~P-'.
c) Are there any outliers in the small cars data set? Use the 1.5 x IQR rule to check and justify your amwer.
'/e-5, out" mod',+.ed. b())( p\crt Shol>)ed a: n -~ .1.. \\ OM. U'f ···n'\£ S~ CC\f.S
i4- 1.5(3)= aq. 5 "hc,.d W'l\t)S be\ow Q~-S bu-\ Q,:. 3lf
Q3~3,, ?>7 -t- 1. 5(3): L/1. 5 ~ 0 C.~"!> wue. c,.Je,f"
4\.Smp~.
IQ~=-'!>
2) Mr. B teaches Algebra I twice a day: I st period
(morning) and~ period (afternoon). Last year, he
compiled his final exam scores for each class period
and found the mean and standard deviation for each
(given in the table to the right). Both of the class
scores were normally distnouted.
Morning Class
Afternoon Class
Mean
82.6
75.8
Standard
Deviation
4.65
7.48
a) On the normal graphs below, draw out each distribution, going out three standard deviations on each side.
Morning Class Afternoon Class
l
a) Nicole was in the morning class and got a score of
90 on the final. Steven was in the afternoon class and
got a score of87 on the final. Who's was the more
impressive score? Explain.
N,c.o\~ S-t~
~~ qO-~.fo ~: --a,-75,g
4.C,5 ,.'4i
8ecoWS~ ~,~o\e. wos -More
b) If a student got a score of 75 in the morning class's
final, what grade would they need to get in the
afternoon class to have the same comparative grade?
Show your work.
~ ft1Cr't\. = 7 5-i~. '1
4-~~
e""--:. - I. qO)::: P(~ :> 90;''')
? (~ ;>1.31s) =fo. o i:aj
