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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:

### 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

(a) Draw a histogram for the grouped frequency distribution in the table.

(b) Calculate the mean, standard deviation and median of the data (you must show your working), and interpret your results.

Mean: 42.3125

Sd: 25.295

Median: 36.8

positive skew in the distribution.

(c) What is the probability that orders exceed 50 per day.

P(orders >50) = 0.35

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