MEASURES OF DISPERSION



Problems on Measures of Dispersion

1. From the following data.

8 7 14 6 13 24 16 9 18 5 10 12

Compute

a. Range

b. Inter-quartile range

c. Quartile deviation.

d. Interfractile range between 20th percentile and 45th percentile.

2. From the following frequency distribution of marks obtained by students in business communication.

|Marks |20-30 |30-40 |40-50 |50-60 |60-70 |70-80 |80-90 |

|No. of students. |15 |20 |10 |35 |20 |25 |30 |

Compute

a. Range

b. Inter-quartile range

c. Quartile deviation.

d. Interfractile range between 40th percentile and 85th percentile.

3. The following given data are the marks obtained by the students in business statistics.

8 7 14 6 13 24 16 9 18 5 10 12

Calculate

a. Standard deviation

b. Variance

c. Coefficient of variation.

4. In an attempt to estimate potential future demand, the National Motor Company did a study asking married couples how many cars the average energy minded family should own in 1998. For each couple, National averaged the husband’s and wife’s response to get the overall couple response. The answers were then tabulated:

Number of cars: 0 .5 1.0 1.5 2.0 2.5

Frequency : 2 14 23 7 4 2

Calculate the variance, standard deviation and coefficient of variation.

5. Calculate the variance, coefficient of variation and standard deviation form the following frequency distribution.

|class |5-10 |10-15 |15-20 |20-25 |25-30 |

|frequency |6 |9 |20 |24 |11 |

6. For the given sample data compute the

a. range

b. Interfractile range between the 20th and 80th percentiles.

c. Inter quartile range and semi inter quartile range

2549 3897 3661 2697 2200 3812 2228 3891 2668 2268 3692 2145 2653 3249 2841 3469 3268 2598 3842 3362

7. The New Mexico State Highway Department is charged with maintaining all state roads in good condition. One measure of condition is the number of cracks present in each 100feet of roadway. From the department’s yearly sample, the following data were obtained:

4 7 8 9 9 10 11 12 12 13 13 13 13 14 14 14 14 15 15 16 16 16 16 16 17 17 17 18 18 19 19.

a. Calculates the inter-quartile range

b. Plots the box and whisker and discuss the shape of the above distribution.

8. Talent, Ltd., a Hollywood casting company, is selecting a group of extras for a movie. The ages of the first 20 men to be interviewed are

50 56 55 49 52 57 56 57 56 59 54 55 61 60 51 59 62 52 54 49

The director of the movie wants men whose ages are fairly tightly grouped around 55 years. Being a statistics buff of sorts, the director suggests that a standard deviation of 3 years would be acceptable. Does this group of extras qualify?

9. The head chef of The Flying Taco has just received two dozen tomatoes from her supplier, but she isn’t ready to accept them. She knows from the invoice that the average weight of a tomato is 7.5 ounces, but she insists that all be of uniform weight. She will accept them only if the average weight is 7.5 ounces and the standard deviation is less than .5 ounce. Here are the weights of the tomatoes:

6.3 7.2 7.3 8.1 7.8 6.8 7.5 7.8 7.2 7.5 8.1 8.2 8.0 7.4 7.6 7.7 7.6 7.4 7.5 8.4 7.4 7.6 6.2 7.4

What is the chef’s decision and why?

10. These data are a sample of the daily production rate of fiberglass boats from Hydrosport, Ltd., a Miami manufacturer:

17 21 18 27 17 21 20 22 18 23

The company production manager feels that a standard deviation of more than three boats a day indicates unacceptable production rate variations. Should she be concerned about plant production rates?

11. The number of checks cashed each day at the five branches of the band of Orange County during the past month had the following frequency distribution:

|Class |0-199 |200-399 |400-599 |600-799 |800-999 |

|Frequency |10 |13 |17 |42 |18 |

Hank Spivey, director of operations for the bank, knows that a standard deviation in check cashing of more than 200 checks per day creates staffing and organizational problems at the branches because of the uneven workload. Should Hank worry about staffing next month?

12. The administrator of a Georgia hospital surveyed the number of days 200 randomly chosen patients stayed in the hospital following an operation. The data are:

Hospital stay I days: 1-3 4-6 7-9 10-12 13-15 16-18 19-21 22-24

Frequency : 18 90 44 21 9 9 4 5

a. Calculate the mean and standard deviations.

b. Variance and C.V.(Coefficient of variation)

13. Fund info provides information to its subscribers to enable them to evaluate the performance of mutual funds they are considering as potential investment vehicles. A recent survey of funds whose stated investment goal was growth and income produced the following data on total annual rate of return over the past five years:

|Annual return (%) |11-11.9 |12-12.9 |

|Mean |65 units |72 units |

|Standard deviation |13 units |18 units |

|Number of households |50 |40 |

a) Which set is more variable?

b) Calculate the coefficient of variation of the combined set.

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download