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Advertising Age annually compiles a list of the 100 companies that spend the most on advertising. Consumer-goods company Procter & Gamble has often topped the list, spending billions of dollars annually (Advertising Age website, March 12, 2013). Con- sider the data found in the DATAfile named Advertising. It contains annual advertising expenditures for a sample of 20 companies in the automotive sector and 20 companies in the department store sector. What is the mean advertising spent for each sector? What is the standard deviation for each sector? What is the range of advertising spent for each sector? What is the interquartile range for each sector? Based on this sample and your answers to parts (a) to (d), comment on any differences in the advertising spending in the automotive companies versus the department store companies.

Respuesta :

fichoh

Using the appropriate statistical relationship, the mean, range and Interquartile range for the advertisement spending of the two companies are worked out below.

Automotive:

598, 1512, 1573, 1642, 1714, 1720, 1781, 1798, 1813, 2008, 2014, 2024, 2058, 2166, 2202, 2254, 2366, 2526, 2531, 2901

Department :

448, 472, 474, 573, 589, 597, 598, 622, 629, 669, 706, 714, 746, 760, 782, 824, 840, 856, 947, 1011

Recall :

Sample mean = ΣX/n

  • n = sample size

1.)

Mean for Automotive = 39201 / 20 = 1960.05

Mean for Department = 13857 / 20 = 692.85

2.)

  • Range = Maximum - Minimum

Range for Automotive = 2901 - 598 = 2303

Range for Department = 1011 - 448 = 563

3.)

  • Interquartile Range = Upper - Lower quartile

Automotive :

Upper quartile(Q3) = 0.75(21) = 15.75th term = 2228

Lower quartile (Q1) = 0.25(21) = 5.25th term = 1717

Interquartile Range = 2228 - 1717 = 511

Department :

Upper quartile(Q3) = 0.75(21) = 15.75th term = 803

Lower quartile (Q1) = 0.25(21) = 5.25th term = 593

Interquartile Range = 893 - 593 = 210

4.)

Comparing the spread of the spending between the companies, the average spending by the Automotive company is higher with a greater level of spread.

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