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CHAPTER 7 1.
Name the four kinds kinds of useful information information that that you can get about a set of measurement measurement data once once it has been organized and summarized. ANSWER: 1) THE CENTER; 2) THE VARIABILITY; 3) THE SHAPE; AND 4) UNUSUAL VALUES (OUTLIERS).
Narrative: Quiz scores Bob has taken 6 quizzes so far in his statistics class. Each quiz has a ossible of 1! total oints. Bob"s scores are the follo#ing: 1!$ %$ &$ '$ ($ and &. (.
)Quiz scores narrative* narrative* +ind +ind the three three measures measures of center center for Bob"s Bob"s quiz quiz scores. scores. ANSWER: THE MEAN (AVERAGE) IS 7.; THE MODE IS !; THE MEDIAN IS "..
,.
)Quiz scores narrative* narrative* E-lain E-lain ho# if/ if/ Bob"s lo#est quiz quiz score score affects the mean and and the median median of this data set. ANSWER: THE 2 BRINGS DOWN THE MEAN (AVERAGE); IT DOES NOT A##ECT THE MEDIAN.
0.
hich hich of the follo#in follo#ing g measur measures es of center center is affect affected ed by an outlier outlier22 a. 3ean b. 3edian c. 3ode d. 4ll 4ll of the the ab above ANSWER: A
5.
he mode is most most meani meaningf ngful ul for for #hich #hich tye tye of data2 data2 a. 3ea 3easure sureme ment nt data data b. 7ate 7atego gorrical ical data data c. Biased data d. Non None of of the the abo above ANSWER: B
6.
he amount amount of sread sread in in the data data is a measure measure of #hat characteristic characteristic of a data set2 a. 7enter b. 8ariability c. 9hae d. Non None of of the the abo above ANSWER: B
'.
ne or t#o scores that are far far removed removed from the rest of the data data are called called ;;;;;;; ;;;;;;;;;;. ;;;. ANSWER: OUTLIERS
Narrative: 9chool costs 9uose a random samle of liberal arts schools #as taken$ and the average cost er student #as measured for each school. he data are ictured in the histogram belo#:
Cost Per Student: Liberal Arts
12 10 8 6 4 2 0
0 0 0 RESPONSE #REE 0 0 0 0 0 0 0 0 $UESTIONS 0 0 0 0 0 o r e 0 0 0 0 0 0 0 0 0 0 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0 M %. )9chool cost narrative* hat is the shae of this data set2 ANSWER: S%EWED TO THE RIGHT. DATA ALSO HAS AN OUTLIER ON THE HIGH END. &.
)9chool cost narrative*
1!. )9chool cost narrative* #o measures of center #ere calculated for this data set and #ere found to be =(6$66%$ and =,0$%,(. ne of them is the mean$ and the other is the median. hich one is #hich$ and ho# do you kno# that2 ANSWER: &2'''" IS THE MEDIAN AND &34"32 IS THE MEAN. WHY: THE DATA IS S%EWED TO THE RIGHT AND HAS AN OUTLIER BOTH O# WHICH DRIVE UP THE MEAN AND LEAVE THE MEDIAN UNA##ECTED. 11. hich of the follo#ing ictures of a data set allo#s you to retrieve the actual data assuming no digits are droed/2 a. 4 histogram b. 4 stemlot c. Both a/ and b/ d. Neither a/ nor b/ ANSWER: B 1(. >f the bars of a histogram reresent the roortion of the total count that falls into each interval$ #hat must the heights of the bars sum to2 a. he total number of numbers in the data set. b. ne. c. 1 divided by the total number of intervals used in the histogram. d. Not enough information to tell. ANSWER: B 1,. hich of the follo#ing statements is true2 a. >f a data set is ske#ed to the right$ that means there is bias in the results? the data are higher than they should be. b. >f a data set is ske#ed to the right$ then the higher values are more sread out than the lo#er values. c. >f a data set is ske#ed to the right$ then the lo#er values are more sread out than the higher values. d. None of the above. ANSWER: B
10. hich of the follo#ing statements regarding stemlots is false2 a. b. c.
4 stemlot allo#s you to retrieve the original data assuming no digits are droed/. 4 stemlot can never reuse the same stem digit t#ice. >f a certain value in your data set is reeated three times$ it must aear , times in aroriate stem and leaf of the stemlot. d. None of the above statements are false. ANSWER: B
15. 4 ;;;;;;;;;; is a quick and easy #ay to ut a list of numbers into order #hile getting a icture of their shae. ANSWER: STEMPLOT 16. 4 data set is ;;;;;;;;;; if the t#o halves of the data set #hen cut do#n the middle/ are mirror images of each other. ANSWER: SYMMETRIC 1'. hat are the five numbers used in a five@number summary2 ANSWER: THE LOWEST (MINIMUM); THE HIGHEST (MAIMUM); THE MEDIAN; THE LOWER $UARTILE; AND THE UPPER $UARTILE.
Narrative: 4ccetance rates 4 random samle of 5! colleges and universities in the A.9. #as selected$ and accetance rates #ere recorded for each school ercentage of student alicants #ho #ere acceted to the school/. he follo#ing five@number summary #as calculated for this data set: lo#est 1'? lo#er quartile (5.'5? median ,6? uer quartile 0'.'5? highest 6'. 1%. )4ccetance rates narrative* Cescribe the shae of this data based on the five@number summary. ANSWER: THE DATA SET LOO%S #AIRLY EVENLY DISTRIBUTED ECEPT #OR THE LAST $UARTER O# THE DATA WHICH IS MORE SPREAD OUT THAN THE REST INDICATING S%EWNESS TO THE RIGHT. 1&. )4ccetance rates narrative* Cescribe the center of this data set in #ords a rosective student #ould understand. ANSWER: THE MEDIAN (MIDDLE) O# THE ACCEPTANCE RATES IS 3'*. ABOUT HAL# O# THE SCHOOLS ACCEPT 3'* OR MORE O# APPLICANTS AND ABOUT HAL# ACCEPT 3'* OR LESS. (!. )4ccetance rates narrative* +ind the range of the accetance rates and give one ossible reason that it is such a high number. ANSWER: RANGE + ,; EPLANATION: ANY REASONABLE ANSWER O%. EAMPLES: AN OUTLIER WOULD A##ECT THE RANGE; THERE ARE MANY VARIABLES A##ECTING ACCEPTANCE RATES INCLUDING TYPE O# INSTITUTION (LIBERAL ARTS VS. #OUR-YEAR UNIVERSITY ETC); REGION O# THE U.S.; $UALITY O# EDUCATION; ETC.
(1. 9uose that in a five@number summary you find that a larger ga e-ists bet#een the third quartile and the highest value than bet#een the lo#est value and the first quartile. hat does this mean about the shae of the data set2 a. 9ymmetric b. 9ke#ed right c. 9ke#ed left d. Not enough information to tell. ANSWER: B
((. hich of the follo#ing does not require the data to be ordered before you can get the right ans#er2 a. 3ean b. 3edian c. Quartiles d. Dange e. 4ll of the above require the data to be ordered. ANSWER: A
(,. he ;;;;;;;;;; are the medians of the t#o halves of an ordered data set. ANSWER: $UARTILES (0. 4 five@number summary involves the lo#er quartile$ the uer quartile$ the lo#est number$ the highest number$ and the ;;;;;;;;;;. ANSWER: MEDIAN (5. Cescribe #hich numerical summaries statistics/ of a dataset a bo-lot is based uon. ANSWER: THE #IVE-NUMBER SUMMARY (LOWEST NUMBER LOWER $UARTILE MEDIAN UPPER $UARTILE AND HIGHEST NUMBER).
Narrative: iberal arts costs 4 random samle of (5 liberal arts colleges in the A.9. #as selected$ and the average cost er student #as recorded for each school. he follo#ing five@number summary #as calculated for this data set: lo#est =1'$550? lo#er quartile =(,$115? median =(6$66%? uer quartile =05$%'&? highest =1!($(6(. (6. )iberal arts costs narrative* 3ake a bo-lot of this data set and use it to discuss the shae of the data. ANSWER: BOPLOT SHOULD HAVE A BO AROUND THE UPPER AND LOWER $UARTILES WITH A LINE DOWN THE MIDDLE #OR THE MEDIAN AND LINES GOING OUT TO THE LOWEST AND HIGHEST VALUES CONNECTING WITH THE BO ALL IN THE PROPER SCALE. SHAPE: S%EWED RIGHT. ('. )iberal arts costs narrative* Asing the statistical rule discussed in your te-tbook$ is there an outlier in this data set2 E-lain your ans#er. ANSWER: YES. THE HIGHEST AMOUNT &1,22'2 IS MORE THAN 1. TIMES THE I$R AWAY #ROM THE UPPER END O# THE BO.
(%. f the #idth of a bo- in a bo-lot is very large$ comared to the rest of the bo-lot$ #hat does that mean about the shae of the data set2 a. he data are very sread out in the middle. b. he data are clumed tightly in the middle. c. he data are not symmetric. d. Not enough information to tell. ANSWER: A
,!. 9uose you look at t#o bo-lots comaring the #eights of male cats vs. female cats$ and you find that the bo- for the males is much #ider than the bo- for the females. hat does this mean about the data sets2 a. 3ale cats #eigh more than female cats overall. b. 3ale cats have more variability in their #eights than female cats. c. eights of male cats are more ske#ed than for female cats. d. None of the above. ANSWER: B ,1. 4n/ ;;;;;;;;;; is any value that is more than 1.5 times the >QD from the closest end of the bo- in a bo-lot. ANSWER: OUTLIER
Narrative: 7reate data 9uose you can create your o#n data set by choosing from the numbers 1$ ($ ,$ 0$ and 5. Fou can reeat a number as many times as you #ish$ as long as your final data set contains four numbers in it.
,5. hat is the relationshi bet#een the variance and the standard deviation2 a. he variance is the square root of the standard deviation. b. he variance is the square of the standard deviation. c. he variance is t#ice the standard deviation. d. here is no relationshi bet#een them. ANSWER: B ,6. 9uose a data set is ske#ed left. hat is the most likely relationshi bet#een the mean and the median2 a. he mean is larger than the median. b. he mean is smaller than the median. c. he mean and the median are not related to each other at all. d. he mean and the median are essentially equal. ANSWER: B ,'. hich of the follo#ing statements is false2 a. >f the standard deviation is ositive$ the mean must be ositive. b. he standard deviation can be negative. c. >f the mean is large$ the standard deviation #ill be large also. d. 4ll of the above are false. ANSWER: D
,%. hich of the follo#ing is not a measure of sread or variability in a data set2 a. 9tandard deviation b. >QD c. Dange d. 4ll of the above are measures of sread or variability in a data set. ANSWER: D
,&. Because the ;;;;;;;;;; can be distorted by high outliers$ the center of a data set involving incomes or rices is usually summarized using the ;;;;;;;;;;. ANSWERS (RESPECTIVELY): MEAN MEDIAN 0!. >f the shae of a data set is ;;;;;;;;;; then the mean and the median should be about equal. ANSWER: SYMMETRIC
01. >f you Gust use an average to describe a set of measurements$ is this enough2 E-lain your ans#er. ANSWER: NO; YOU ALSO NEED TO ADDRESS THE AMOUNT O# VARIABILITY IN THE DATA.
