BRIEF SOLUTIONS

Numerical Descriptive

Measures

WEEK TWO

This worksheet relates to chapter three of the text

book (Statistics for Managers 4th Edition).

Past exam questions are very important to give you

an idea of what to expect in an exam and how

prepared you are. You may need to practice doing

questions quickly so that when you are in the exam

you don’t panic.

CALCULATION QUESTIONS

1. Using the following data to calculate the mean, median, mode, 1st quartile

and 3rd quartile. Are there any outliers?

5 7 8 9 9 9 9 10 10 12 40

Mean: Median:

11.63 position = 6

value = 9

Mode: 1st quartile:

9 position = 3

value = 8

3rd quartile: Outliers:

position = 9 40

value = 10

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2. The price of renting a car for a week, with manual transmission but

declining collision damage waiver in 12 European countries is presented

in the table. Calculate the mean and interquartile range.

Country Rental Price

Austria 239

Belgium

Britain 179

Denmark

France 229

Ireland

Netherlands 181

Norway

237

Spain

Sweden 216

Switzerland

Germany 194

241

154

280

254

192 Mid Semester, April 2005

In order:

154 179 181 192 194 216 229 237 239 241 254 280

Mean: 216.33

IQ range:

Q1 position: 3.25

Q1 value: 181 (ie. 3rd score)

Q3 position: 9.75

Q3 value: 241 (ie. 10th score)

∴ IQ range = 241 – 181

= 60

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At the end of each chapter of the textbook

there is a summary flow chart. They can be

really useful to work out exactly how all of

the concepts fit together.

3. Calculate the coefficient of variation for the following two sets of data

using the given information. Which has greater variation? Why do we

use the coefficient of variation here, and not the standard deviation or

variance?

Grams of cereal 400 392 415 387 407

Kilograms of rock 4000 4365 3625 4184 3748

Cereal Rock

Mean = 400.2 Mean = 3984.4

SD = 11.256 SD = 304.135

CV = 2.81% CV = 7.633%

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MULTIPLE CHOICE PRACTICE

1. An error has been made in the scaling of exam marks, and five extra

marks are given to every student. The result is that:

(a) The mean score increases by 5 but the standard deviation does

not change

(b) Both the mean and the standard deviation increase by 5

(c) The mean increases by 5 and the standard deviation increases by

sqrt5

(d) The mean and variance increase by 5 Final Exam, June 2003

Final Exam, June 1997

2. The correlation coefficient between the price of broccoli and the amount

of rain that fell during the growing season is calculated to be -0.878. This

indicates that

(a) a large amount of rain causes high prices

(b) prices tend to be low when rainfall is high

(c) prices tend to high when rainfall is high

(d) a lack of rain causes prices to rise

Final Exam, June 2004

3. A student scored 70% on the mid-semester exam, 83% on the CML’s

and 76% on the final exam. Find the average score if the mid-semester

exam was worth 25% and the final exam was worth 55%.

(a) 76.3% Mid Semester, April 2000;

(b)75.9% Mid Semester, May 2003

(c) 78.35%

(d) 71.75%

4. The geometric mean

(a) is a better measure of dispersion than the arithmetic mean

(b) is preferable to an arithmetic mean when the data fluctuates

between positive to negative

(c) indicates the multiplicative effects over time in compound

interest situations

(d) both (b) and (c) are true Mid Semester, April 2005

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5. The following is the descriptive statistics printout for a set of data, from

Excel.

Mean 473.4615

Median 451

Mode n/a

Standard Deviation

Minimum 210.7663

Maximum 264

Sum 1049

Count 6155

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Which of the following is true?

(a) the distribution is right-skewed

(b) the best measure of central tendency is the median

(c) both (a) and (b) are correct

(d) none of the above are correct

Mid Semester, April 2005

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notes

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