Financial Stocks 1893 538 2100 791 4048 1537 4342 1583 2705

Financial Stocks

18.93

5.38

21.00

7.91

40.48

15.37

43.42

15.83

27.05

15.23

48.12

11.91

43.37

14.65

46.32

9.76

24.01

19.24

29.23

7.94

Energy Stocks

21.03

26.14

11.25

16.75

21.74

20.31

23.82

23.51

12.46

21.16

21.46

26.65

10.27

20.82

26.58

13.91

26.62

24.39

19.07

19.07

Stocks can be categorized by industry. The following data represent the 5-year rates of return for a simple random sample of financial stocks and energy stocks.

Compute the mean and median rate of return for each industry. Which sector has the higher mean rate of return? Which sector has the higher median rate of return?

Sample mean for financial stocks =

Sample mean for energy stocks =

Median for financial stocks =

Median for energy stocks =

Which sector has the higher mean rate of return?

The energy or financial stocks have the higher mean rate of return

Which sector has the higher median rate of return?

The energy or financial stock has the higher median rate of return

Compute the standard deviation for each industry. In finance, the standard deviation rate of return is called risk. Which sector is riskier?

Sample standard deviation for financial stocks =

Sample standard deviation for energy stocks =

Which of the stocks are riskier financial or energy?

Financial Stocks
18.93	5.38	21.00	7.91	40.48
15.37	43.42	15.83	27.05	15.23
48.12	11.91	43.37	14.65	46.32
9.76	24.01	19.24	29.23	7.94
Energy Stocks
21.03	26.14	11.25	16.75	21.74
20.31	23.82	23.51	12.46	21.16
21.46	26.65	10.27	20.82	26.58
13.91	26.62	24.39	19.07	19.07

Solution

Stocks can be categorized by industry. The following data represent the 5-year rates of return for a simple random sample of financial stocks and energy stocks.

Compute the mean and median rate of return for each industry. Which sector has the higher mean rate of return? Which sector has the higher median rate of return?

financial

(x-mean)

(x-mean)^2

energy

(x-mean)

(x-mean)^2

5.38

-17.8775

319.6050063

10.27

-10.0805

101.6164803

7.91

-15.3475

235.5457563

11.25

-9.1005

82.81910025

7.94

-15.3175

234.6258063

12.46

-7.8905

62.25999025

9.76

-13.4975

182.1825063

13.91

-6.4405

41.48004025

11.91

-11.3475

128.7657563

16.75

-3.6005

12.96360025

14.65

-8.6075

74.08905625

19.07

-1.2805

1.63968025

15.23

-8.0275

64.44075625

19.07

-1.2805

1.63968025

15.37

-7.8875

62.21265625

20.31

-0.0405

0.00164025

15.83

-7.4275

55.16775625

20.82

0.4695

0.22043025

18.93

-4.3275

18.72725625

21.03

0.6795

0.46172025

19.24

-4.0175

16.14030625

21.16

0.8095

0.65529025

21

-2.2575

5.09630625

21.46

1.1095

1.23099025

24.01

0.7525

0.56625625

21.74

1.3895

1.93071025

27.05

3.7925

14.38305625

23.51

3.1595

9.98244025

29.23

5.9725

35.67075625

23.82

3.4695

12.03743025

40.48

17.2225

296.6145063

24.39

4.0395

16.31756025

43.37

20.1125

404.5126563

26.14

5.7895

33.51831025

43.42

20.1625

406.5264063

26.58

6.2295

38.80667025

46.32

23.0625

531.8789063

26.62

6.2695

39.30663025

48.12

24.8625

618.1439063

26.65

6.2995

39.68370025

sum:

465.15

3704.895375

407.01

498.572095

To find these values, set up a table sorted lowest to highest. Have a column for financial and a column for energy. Then for each, make a new column where you subtract the mean from them, and finally a column for squaring those values. Then using the last row, the totals, and the sample size of 20, you can compute as follows:

Sample mean for financial stocks = 465.15/20 = 23.2575

Sample mean for energy stocks =407.01/20 = 20.3505

The median is the middle value. Since the sample size is 20, an even number, it will be the average of the two middle numbers

Median for financial stocks = (18.93 + 19.24)/2 = 19.085

Median for energy stocks = (21.03 + 21.16)/2 = 21.095

Which sector has the higher mean rate of return?

The financial stocks have the higher mean rate of return. (23.2575 is greater than 20.3505)

Which sector has the higher median rate of return?

The energy stock has the higher median rate of return (21.095 is greater than 19.085)

Compute the standard deviation for each industry. In finance, the standard deviation rate of return is called risk. Which sector is riskier?

To compute this, use the last row, the sums and the sample size of 20.

Sample standard deviation for financial stocks = square root of (3704.895375/(20-1)) = 13.964

Sample standard deviation for energy stocks = square root of (498.572095/(20-1)) = 5.123

Which of the stocks are riskier financial or energy? Financial is riskier, 13.964 is greater than 5.123

	financial	(x-mean)	(x-mean)^2	energy	(x-mean)	(x-mean)^2
	5.38	-17.8775	319.6050063	10.27	-10.0805	101.6164803
	7.91	-15.3475	235.5457563	11.25	-9.1005	82.81910025
	7.94	-15.3175	234.6258063	12.46	-7.8905	62.25999025
	9.76	-13.4975	182.1825063	13.91	-6.4405	41.48004025
	11.91	-11.3475	128.7657563	16.75	-3.6005	12.96360025
	14.65	-8.6075	74.08905625	19.07	-1.2805	1.63968025
	15.23	-8.0275	64.44075625	19.07	-1.2805	1.63968025
	15.37	-7.8875	62.21265625	20.31	-0.0405	0.00164025
	15.83	-7.4275	55.16775625	20.82	0.4695	0.22043025
	18.93	-4.3275	18.72725625	21.03	0.6795	0.46172025
	19.24	-4.0175	16.14030625	21.16	0.8095	0.65529025
	21	-2.2575	5.09630625	21.46	1.1095	1.23099025
	24.01	0.7525	0.56625625	21.74	1.3895	1.93071025
	27.05	3.7925	14.38305625	23.51	3.1595	9.98244025
	29.23	5.9725	35.67075625	23.82	3.4695	12.03743025
	40.48	17.2225	296.6145063	24.39	4.0395	16.31756025
	43.37	20.1125	404.5126563	26.14	5.7895	33.51831025
	43.42	20.1625	406.5264063	26.58	6.2295	38.80667025
	46.32	23.0625	531.8789063	26.62	6.2695	39.30663025
	48.12	24.8625	618.1439063	26.65	6.2995	39.68370025
sum:	465.15		3704.895375	407.01		498.572095