Exercises: Summarising and Presenting Data

1. What type of variable is each of the following?

1. hair colour
2. number of television sets in a private home
3. possible responses to questionnaire items are: yes, no, don't know
4. earthquake intensity
5. final position in a race - 1st, 30th, etc.

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2. A marketing consultant recorded the amount of money spent by 20 consecutive shoppers in a grocery store. The amounts (in dollars) in increasing order were:

6.61	6.90	8.04	9.45	10.26	11.63	12.95	13.67	14.35	14.55
15.01	15.33	16.55	18.22	18.30	19.54	20.58	20.89	21.13	33.80.

1. Draw a stem and leaf plot for these data. (Hint: truncate the data first.)
2. What are the mean and median amounts of money spent by shoppers?

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3. If the mean weight for 20 packages mailed today by the shipping department of a manufacturing company is 60 kilograms, what is the total weight of all the packages ?

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4. A portfolio manager buys the following stocks: 150 shares of General Motors at $65 per share, 100 shares of International Business Machines at $250 per share and 200 shares of Shell Oil at $75 per share. What is the mean price per share purchased ?

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5. A frequency distribution of the length of telephone calls monitored at the switchboard of an office is given below. Compute the arithmetic mean and standard deviation of the calling time.

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6. (a) Calculate the interquartile range (IQR) of these data, which are already sorted:

10,15,17,17,20,24,32,41

(b) Calculate the standard deviation of the same data.

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7. Find the proportion of the standard normal distribution in the following areas (draw the curve and shade the area required)

1. less than 0
2. greater than -0.68
3. less than 1.62
4. between 1 and 2
5. greater than 2.14
6. between -1.5 and 0.84

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8. Find Z values such that the proportion of the standard normal curve less then that value is

1. 0.99
2. 0.90
3. 0.75
4. 0.5
5. 0.05
6. 0.01

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9. Repeat question 8 using the N(10,4) curve.

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10. The number of days sick leave requested annually by employees of a large insurance company is normally distributed with a mean of 9 days and standard deviation of 2.5 days.

• What proportion of the employees request at least 10 days sick leave ?
• If the company employs 600 people, how many use fewer than 2 days sick leave annually?
• Find the 90th percentile of the distribution.

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11. Plot a scatter plot and calculate the correlation coefficient for the following 'data'.

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12. A study was conducted to investigate the relationship between resale price y (in hundreds of dollars) and the age x (in years) of midsize luxury American made cars. The equation of the line of best fit was y = 185.7 - 21.52x

1. Find the resale price of such a car when it is 3 years old.
2. Find the resale price of such a car when it is 6 years old.
3. Interpret the meaning of the slope coefficient -21.52 in the context of this problem.

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13. Given the simple linear regression model y = a + bx describe realistic variables x and y for which you would expect

• b to be positive
• b to be negative
• b to be zero.

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14. Consider the death rates for American males in the 15 to 24 year-old age group from 1914 to 1921 (number of deaths per thousand per year).

Year	1914	1915	1916	1917	1918	1919	1920	1921
death rate	4.4	4.2	4.5	5.0	12.2	5.3	4.8	3.8

1. Plot the death rate against time.
2. Smooth using 3 year moving averages.
3. Smooth using 3 year running medians.
4. Comment on the results of the smoothing.

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15. At the Computer Corporation, records classify each employee according to the variable qualifications which indicates the highest academic level attained by each employee (1 = high school, 2 = college, 3 = university) and division in which the employee works (1 = office, 2 = manufacturing, 3 = sales). The data show

• Consider the employees with high school qualifications only. What proportion are employed in sales ?
• Consider the employees with college qualifications. What proportion are employed in the office ?
• Consider the employees in manufacturing. What proportion have high school qualifications only ?
• What proportion of the companys employees work in sales ?

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