A price-earnings ratio or P/E ratio is calculated as a firm’s share price compar

Question

A price-earnings ratio or P/E ratio is calculated as a firm’s share price compared to the income or profit earned by the firm per share. Generally, a high P/E ratio suggests that investors are expecting higher earnings growth in the future compared to companies with a lower P/E ratio. The accompanying table shows a portion of companies that comprise the Dow Jones Industrial Average (DJIA) and their P/E ratios as of May 17, 2012 (at the time data were retrieved, the P/E ratio for one firm on the DJIA, Bank of America, was not available).

Calculate the 25th, 50th, and 75th percentiles. (Do not round intermediate calculations. Round your answers to 1 decimal place.)

Calculate the IQR, lower limit and upper limit to detect outliers. (Round your intermediate calculations to 4 decimal places and final answers to 2 decimal places.)

A price-earnings ratio or P/E ratio is calculated as a firm’s share price compared to the income or profit earned by the firm per share. Generally, a high P/E ratio suggests that investors are expecting higher earnings growth in the future compared to companies with a lower P/E ratio. The accompanying table shows a portion of companies that comprise the Dow Jones Industrial Average (DJIA) and their P/E ratios as of May 17, 2012 (at the time data were retrieved, the P/E ratio for one firm on the DJIA, Bank of America, was not available).

Explanation / Answer

a)

Following is the ordered data set:

Sicne there are 29 data values so median (50th percentile) will 15th data value so

median = 50th percentile = 15

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First quartile will be middle value of first half of data set. Since there are 29 data values so first quartile will be 8th data value. That is first quartile (25 th percntile) will be

25th percentile = 12

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Third quartile will be middle value of second half of data set. Since there are 29 data values so third quartile will be 22nd data value. That is third quartile (75 th percentile) will be

75th percentile = 19

The IQR:

IQR = 75th percentile - 25th percentile = 19 - 12 = 7

Lower fence :

LF = 25th percnetile -1.5 IQR = 12 - 7 *1.5 = 1.5

Upper fence :

UF = 75th percnetile +1.5 IQR = 19 + 7 *1.5 = 29.5

Outliers: 44, 49

P/E Ratio 7 8 8 10 11 11 11 12 12 13 13 13 14 14 15 15 16 17 17 17 18 19 19 20 20 21 24 44 49

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