27.EM1 A price-earnings ratio or P/E ratio is calculated as a firm’s share price

Question

27.EM1

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. (Negative value should be indicated by a minus sign. 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. Arrange data in ascending order.

There are 29 data. Thus, for odd numbered data, the median or 50th percentile is the middlemost value. Thus, median, M=15th value in the data set=15. The 25th percentile refer to the median of the upper part (above 50th percentile) of the data. Thus, for upper half of data which is even in number, the 25th percentile is the average of the 7th and 8th data value. Thus, 25th percentile is:(11+12)/2=11.5. Similarly, the 75th percentile is the median of the lower half of the data. Thus, 75th percentile is average of 22nd and 23rd data. Thus, 75th percentile is:(19+19)/2=19

b.1 IQR=Q3-Q1=19-11.5=7.5

Lower boundary: Q1-1.5IQR=11.5-1.5*7.5=0.25

Upper boundary: Q3+1.5IQR=19+1.5*7.5=30.25

b-2 Any value beyound the lower and upper boundary is considered outliers. Therefore, 44 and 49 are two possible outliers. Ans>Yes.

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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