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Chapter 2: Q40. (page 94)

Calculate the mode, mean, and median of the following data:

18 10 15 13 17 15 12 15 18 16 11

Short Answer

Expert verified

Mean = 14.54

Median = 15

Mode = 15

Step by step solution

01

Calculating the mean

Mean can be computed using the formula:

Mean鈥�=鈥�Summation鈥�of鈥�observationsTotal鈥�鈥�number鈥�of鈥�observationsMean鈥�=18+10+15+13+17+15+12+15+18+16+1111Mean鈥�=鈥�14.54

Therefore, the mean is 14.54.

02

Computing the median

Median is the central value when the total number of observations in a series is an odd number. In the given case, the total terms are 11 (Odd). Therefore, the median will be the middle value in the series when arranged in ascending order.

Arranging the data in ascending order:

10, 11, 12, 13, 15,15,15,16,17,18,18

Hence, the median is 15.

03

Determining the mode

Mode is the value that has been repeated the highest number of times.

Values

Frequency

18

2

10

1

15

3

13

1

17

1

12

1

16

1

11

1

As can be observed from the table, 15 is repeated 3 times.

Thus, the mode is 15.

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Most popular questions from this chapter

A qualitative variable is measured for 20 companies randomly sampled and the data are classified into three classes, small (S), medium (M), and large (L), based on the number of employees in each company. The data (observed class for each company) are listed below. ______________________________________ SSL M SM M S M S L M S SSS M L S L ----------------------------------------------------------------

a. Compute the frequency for each of the three classes.

b. Compute the relative frequency for each of the three classes.

c. Display the results, part a, in a frequency bar graph.

d. Display the results, part b, in a pie chart.

Network server downtime.A manufacturer of network computer server systems is interested in improving its customer support services. As a first step, its marketing department has been charged with the responsibility of summarizing the extent of customer problems in terms of system downtime. The 40 most recent customers were surveyed to determine the amount of downtime (in hours) they had experienced during the previous month. These data are listed in the table.

Customer Number

Downtime

Customer Number

Downtime

230

12

250

4

231

16

251

10

232

5

252

15

233

16

253

7

234

21

254

20

235

29

255

9

236

38

256

22

237

14

257

18

238

47

258

28

239

0

259

19

240

24

260

34

241

15

261

26

242

13

262

17

243

8

263

11

244

2

264

64

245

11

265

19

246

22

266

18

247

17

267

24

248

31

268

49

249

10

269

50

a.Construct a box plot for these data. Use the information reflected in the box plot to describe the frequency distribution of the data set. Your description should address central tendency, variation, and skewness.

b.Use your box plot to determine which customers are having unusually lengthy downtimes.

c.Find and interpret the z-scores associated with the customers you identified in part b.

Describe how the mean compares to the median for distribution as follows:

a.Skewed to the left

b.Skewed to the right

c.Symmetric

Salary offers to MBAs.Consider the top salary offer (in thousands of dollars) received by each member of a sample of 50 MBA students who graduated from the Graduate School of Management at Rutgers, the state university of New Jersey. Descriptive statistics and a box plot for the data are shown on the XLSTAT printouts at the top of the next column. [Note:The 鈥�+鈥� on the box plot represents the location of the mean.]

a.Find and interpret the z-score associated with the highest salary offer, the lowest salary offer, and the mean salary offer. Would you consider the highest offer to be unusually high? Why or why not?

b.Based on the box plot for this data set, which salary offers (if any) are suspect or highly suspect outliers?

Question: Given a data set with a largest value of 760 and a smallest value of 135, what would you estimate the standard deviation to be? Explain the logic behind the procedure you used to estimate the standard deviation. Suppose the standard deviation is reported to be 25. Is this feasible? Explain
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