Business statistics Chapter 3

(2)In some reports, the mean and coefficient of variation are given. For instance, one report gives the average number of physician visits by males per year. The average reported is 2.6, and the reported coefficient of variation is 2.9%. Use this information to determine the standard deviation of the annual number of visits to physicians made by males. (Round your answer to three decimal places.)

.0754

When data consist of percentages, ratios, compounded growth rates, or other rates of change, the geometric mean is a useful measure of central tendency. For n data values, the geometric mean, assuming all data values are positive, is as follows. To find the average growth factor over 5 years of an investment in a mutual fund with growth rates of 10.1% the first year, 11.8% the second year, 14.4% the third year, 4.3% the fourth year, and 6.1% the fifth year, take the geometric mean of 1.101, 1.118, 1.144, 1.043, and 1.061. Find the average growth factor of this investment. (Round your answer to four decimal places.) Geometric mean

1.0928

How hot does it get in Death Valley? The following data are taken from a study conducted by the National Park System, of which Death Valley is a unit. The ground temperatures (°F) were taken from May to November in the vicinity of Furnace Creek. Compute the mean, median, and mode for these ground temperatures. (Round your mean to four decimal places.) 148,150,170,176,188,179,180,188,179,170,179,167,150,146

169.2857,173, 179

(2)Each of the following data sets has a mean of x = 10.a) Without doing any computations, order the data sets according to increasing value of standard deviations(i) 8 9 10 11 12(ii) 7 9 10 11 13(iii) 7 8 10 12 13(b) Why do you expect the difference in standard deviations between data sets (i) and (ii) to be greater than the difference in standard deviations between data sets (ii) and (iii)?

1a)(i), (ii), (iii) 1b)The data change between data sets (i) and (ii) increased the squared difference Σ(x - x)2 by more than data sets (ii) and (iii).

Find the weighted average of a data set where 10 has a weight of 5, 40 has a weight of 2, and 50 has a weight of 3.

28

(2)One indicator of an outlier is that an observation is more than 2.5 standard deviations from the mean. Consider the data value 80.(a) If a data set has mean 70 and standard deviation 5, is 80 a suspect outlier?b) If a data set has mean 70 and standard deviation 3, is 80 a suspect outlier?

2a)No, since 80 is less than 2.5 standard deviations above the mean. 2b)Yes, since 80 is more than 2.5 standard deviations above the mean.

(2)Consider sample data with x = 8 and s = 2. (a) Compute the coefficient of variation.b) Compute a 75% Chebyshev interval around the sample mean.

3a)25% 3b) lower limit 4 upper limit 12

(3)Angela took a general aptitude test and scored in the 94th percentile for aptitude in accounting. (a) What percentage of the scores were at or below her score?b) What percentage were above?

4a)94% 4b)6%

When data consist of rates of change, such as speeds, the harmonic mean is an appropriate measure of central tendency. The harmonic mean for n data values, assuming no data value is 0, is given by the equation below. Suppose you drive 51 miles per hour for 100 miles, then 65 miles per hour for 100 miles. Use the harmonic mean to find your average speed. (Round your answer to two decimal places.)

57.16

(3)Consider the following ordered data. 8 11 11 12 13 13 14 15 16 (a) Find the low, Q1, median, Q3, and high b) Find the interquartile range.

5a)Low 8 q1-11 median-3 Q3-14.5 High 16 5b)3.5

In your biology class, your final grade is based on several things: a lab score, scores on two major tests, and your score on the final exam. There are 100 points available for each score. However, the lab score is worth 19% of your total grade, each major test is worth 21.5%, and the final exam is worth 38%. Compute the weighted average for the following scores: 90 on the lab, 64 on the first major test, 94 on the second major test, and 92 on the final exam

86.03

(3)At one hospital there is some concern about the high turnover of nurses. A survey was done to determine how long (in months) nurses had been in their current positions. The responses (in months) of 20 nurses were as follows.33,12,15,24,35,46,37,52,22,18,17,33,39,36,38,21,30,41,18,46 box and wisker. find IQR

Box &whiskers A IQR-19

Find the mean, median, and mode of the data set. 6 2 5 2 4

Mean 3.8,median 4, mode 2

(3)Clayton and Timothy took different sections of Introduction to Economics. Each section had a different final exam. Timothy scored 83 out of 100 and had a percentile rank in his class of 72. Clayton scored 85 out of 100 but his percentile rank in his class was 70. Who performed better with respect to the rest of the students in the class, Clayton or Timothy? Explain your answer.

Timothy, since his percentile score is higher.

Consider the data set 2, 2, 3, 6, 10. (a) Compute the mode, median, and mean. b) Add 5 to each of the data values. c) Compare the results of parts (a) and (b). In general, how do you think the mode, median, and mean are affected when the same constant is added to each data value in a set?

a)2,3,4.5 (b) 7,8,9.6, (c)Adding the same constant c to each data value results in the mode, median, and mean increasing by c units.

(3)What percentage of the general U.S. population have bachelor's degrees? The Statistical Abstract of the United States, 120th Edition, gives the percentage of bachelor's degrees by state. For convenience, the data are sorted in increasing order.17,18,18,18,19,20,20,20,21,21,21,21,22,22,22,22,22,22,23,23,24,24,24,24,24,24,24,24,25,26,26,2626,26,26,27,27,27,27,27,28,28,29,31,31,32,32,34,35,38a) Select the box-and-whisker plot. IQr? c) Illinois has a bachelor's degree percentage rate of about 26%. Into what quarter does this rate fall?

box & whiskers C IQR-5 6c)between the median and Q3

(2)Which average - mean, median, or mode - is associated with the standard deviation?

mean

Which average takes all the specific values into account?

mean

Which average represents the middle value of a data distribution?

median

Which average represents the most frequent value of a data distribution?

mode