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What is the mean price paid for shares by this investor?

1- In June an investor purchased 300 shares of Oracle at $20 a share. In August she purchased an additional 400 shares at $25 per share. In November she purchased another 400 shares at $23. What is the mean price paid for shares by this investor?

2- The five year annualized total returns of six mutual funds are given in the table below, What is the mean return, what is the median return, what is the geometric mean? Is the distribution of returns skewed?

Name of funds	return
PBHG	28.5%
Dean Witter	17.2%
AIM	25.4%
Giftrust	28.6%
Robertson Stevens	22.6%
Seligman	21.0%

Median = 24.

The arithmetic mean = 23.88

Geometric mean = 23.51 – the geometric mean is always less than the arithmetic mean

Mean<median => the distribution is negatively skewed

3-The annual salaries of quality control managers in selected states are shown below. What is the modal annual salary, what is the mean?

state	Salary	state	salary	state	salary
Arizona	$35,000	Illinois	58,000	Ohio	50,000
California	49,100	Louisiana	60,000	Tennessee	60,000
Colorado	60,000	Maryland	60,000	Texas	71,400
Florida	60,000	Massachussetts	40,000	West Virginia	60,000
Idaho	40,000	New Jersey	65,000	Wyoming	55,000

Mode = 60,000

Mean= 54.9

4- Your salary this year is £30,000, your employer promised you a 5% increase this year, and a 15% increase the year after – what will be your salary in two years time – what is the average annual salary increase over the period?

Year 1: 31500

Year 2: 36225

The average salary increase is given by the geometric mean – not the arithmetic one

GM = 1.09886

You can check that 30000 * 1.09886 = 32965.80

32965.8 * 1.09886 = 36224.80 – almost equal to 36225 calculated above.

5- The numbers of traffic offences in Egham over the last 5 weeks are 38, 26, 13, 41, and 22. What is the mean number of offences per week – what is the population variance, standard deviation, range?

Mean = 28,

Variance = 106.8 => sd =10.33

The range is = 28

6- The hourly wages for a sample of part-time employees at fruit packers are £12, £20, £16, £18, and £19. What is the sample variance? What is the sample standard deviation?

Mean =17,

Sample variance = £10, sd = 3.16

7- Listed beloew are the commissions earned last months by a sample of 15 brokers.

2,038 1,758 1,721 1,637 2,097 2,047 2,205 1,787 2,287 1,940 2,311 2,054 2,406 1,471 1,460

Locate the median, first quartile, third quartile and interquartile range for the commissions earned?

Md= 2,308

The first quartile is composed of the first 25% observation:

L25 = 4, so the 4th observation is our 1st quartile value. Q1= 1,721

Similarly L75 =12, Q3= 2,205.

The interquartile range is Q3-Q1 = 484

8- The following are the earnings per share for a sample of 15 software companies for the year 2008. The earnings are ranked from the smallest to the largest.

0.09 0.13 0.41 0.51 1.12 1.20 1.49 3.18 3.50 6.36 7.83 8.92 10.13 12.99 16.40

Compute the mean, median and standard deviation. Is the distribution skewed?

Mean = 4.95

Median = 3.18

Sample standard deviation = 5.22

positively skewed.

9 – The frequency distribution of the vehicle selling prices at Autoplex is the following?

Selling price in £1,000	Frequency
15- <18	8
18- <21	23
21- <24	17
24- <27	18
27- <30	8
30- <33	4
33- <36	2
Total	80

Construct the histogram for the distribution of the prices of vehicle sold. What is the mean price and variance of the vehicle sold? What is the price at which 50% of vehicles were sold for less than that price?

Mean: 23.0625

Variance: 188.013

Half the cars are sold for less than £22,588

10 - The table below shows the frequency distribution for the number of orders received by a company each day based on a random sample of 80 days:

Orders	Number of Days	i M	D=f/i	fM Cf
0 to < 10	5	10 5	0.5	25 5	6961.11
10 to < 20	14	10 15	1.4	210 19	10443.62
20 to < 40	25	20 30	1.25	750 44	3789.94
40 to < 60	16	20 50	0.8	800 60	945.56
60 to < 100	20	40 80	0.5	1600 80	28406.95
Totals	80			3385	50547.18