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From the following data.
8 7 14 6 13 24 16 9 18 5 10 12
Compute
Range
Inter-quartile range
Quartile deviation.
Interfractile range between 20th percentile and 45th percentile.
From the following frequency distribution of marks obtained by students in business communication.
Marks20-3030-4040-5050-6060-7070-8080-90No. of students.15201035202530Compute
Range
Inter-quartile range
Quartile deviation.
Interfractile range between 40th percentile and 85th percentile.
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
Standard deviation
Variance
Coefficient of variation.
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 husbands and wifes 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.
Calculate the variance, coefficient of variation and standard deviation form the following frequency distribution.
class5-1010-1515-2020-2525-30frequency69202411
For the given sample data compute the
range
Interfractile range between the 20th and 80th percentiles.
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
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 departments 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.
Calculates the inter-quartile range
Plots the box and whisker and discuss the shape of the above distribution.
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?
The head chef of The Flying Taco has just received two dozen tomatoes from her supplier, but she isnt 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 chefs decision and why?
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?
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:
Class0-199200-399400-599600-799800-999Frequency1013174218Hank 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?
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
Calculate the mean and standard deviations.
Variance and C.V.(Coefficient of variation)
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 (%)11-11.912-12.913-13.914-14.9-15-15.916-16.917-17.918-18.9frequency2281011831Calculate the mean, variance, standard deviation and C.V. of the annual rate of return for this sample of 45 funds.
Bassart Electronics is considering employing one of two training programs. Two groups were trained for the same task. Group 1 was trained by program A, group 2, by program B. For the first group, the times required to train the employees had an average of 32.11 hours and a variance of 68.09. In the second group, the average was 19.75 hours and the variance was 71.14. Which training program has less relative variability in its performance?
The weights of the Baltimore Bullets professional football team have a mean of 224 pounds with a standard deviation of 18 pounds, while the mean weight and standard deviation of their Sunday Opponent, the Chicago Trailblazers, is 195 and 12, respectively. Which team exhibits the grater relative dispersion in weights?
The University has decided to test three new kinds of light bulbs. They have three identical rooms to use in the experiment. Bulb 1 has an average lifetime of 1470 hours and a variance of 156. Bulb 2 has an average lifetime of 1400 hours and a variance of 81. Bulb 3 has an average lifetime of 1350 hours and a standard deviation of 6 hours. Rank the bulbs in terms of relative variability. Which was the best bulb?
Students ages in the regular daytime M.B.A. program and the evening program of Central University are described by these two samples:
Regular M.B.A.: 13 29 27 22 24 21 25 26 27 24
Evening M.B.A.: 27 34 30 29 28 30 34 35 28 29
If homogeneity of the class is a positive factor in learning, use a measure of relative variability to suggest which of the two groups will be easier to teach.
There are a number of possible measures of sales performance, including how consistent a salesperson is in meeting established sales goals. The data that follow represent the percentage of goal met by each of three salespeople over the last 5 years.
Patricia: 88 68 89 92 103
John : 76 88 90 86 79
Frank : 104 88 118 88 123
Which salesperson is the most consistent?
Human power, the temporary employment agency, has tested many peoples data entry skills. Infotech needs a data entry person, and the person needs to be not only quick but also consistent. Human power pulls the speed records for 4 employees with the data given below in terms of number of correct entries per minute. Which employee is best for Infotech based on relative dispersion?
John: 63 66 68 62 69 72
Jeff: 68 67 66 67 69
Mary: 62 79 75 59 72 84
Tammy: 64 68 58 57 59
Sunray Appliance Company has just completed a study of three possible assembly line configurations for producing its best selling two slice toasters. Configuration 1 has yielded a mean time to construct a toaster of 34.8 minutes and a standard deviation of 4.8 minutes. Configuration 2 has yielded a mean time of 25.5 minutes, and a standard deviation of 7.5 minutes. Configuration 3 has yielded a mean time of 37.5 minutes and a standard deviation of 3.8 minutes. Which assembly line configuration has the least relative variation in the time it takes to construct a toaster?
The Fish and Game station on Lake Wylie keeps records of fish caught on the lake and reports its finding to the National Fish and Game Service. The catch in pounds for the last 20 days was:
101 132 145 144 130 88 156 188 169 130 90 140 130 139 99 100 108 192 165 216
Calculate the range, variance, standard deviation and coefficient of variation.
The owner of Records Anonymous, a large record retailer, uses two different formulas for predicting monthly sales. The first formula has an average miss of 700 records and a standard deviation of 35 records. The second formula has an average miss of 300 records and a standard deviation of 16 records. Which formula is relatively less accurate?
A psychologist wrote a computer program to simulate the way a person responds to a standard IQ test. To test the program, he gave the computer 15 different forms of a popular IQ test and computed its IQ from each form.
IQ values
134 136 137 138 138
143 144 144 145 146
146 146 147 148 153
Calculate the mean, standard deviation, variance and C.V. of IQ scores.
Calculate the inter-quartile range and list the five number summary and plot the box and Whisker.
Allison Barrett does statistical analyses for an automobile racing team. Here are the fuel consumption figures in miles per gallon for the teams cars in recent races:
4.77 6.11 6.11 5.05 5.99 4.91 5.27 6.01 5.75 4.89 6.05 5.22 6.02 6.11 5.02
Calculate the median fuel consumption.
Calculate the mean fuel consumption.
Plot the box and whisker.
The board of directors of a production company is willing to acquire one of the two companies X and Y, and is closely examining the management of each company in regard to their inclination toward risk. During the past five years company X had an average return on investment of 28%, with a standard deviation of 5.3%. Company Y, on this period, had an average return of investment of 37.8% with standard deviation of 4.8%. if we consider risk to be associated with greater relative dispersion which of the companies X or Y had perused a riskier strategy?
The populations mean and standard deviation of the marks in statistics obtained by all the 50 students of a certain college was computed as 60 and 10 respectively. Later on it was discovered that the score 76 was wrongly taken as 67. Find the correct mean and standard deviation after correction.
The following data are the marks in statistics obtained by the entire 100 students at college X.
Marks below: 10 20 30 40 50 60 70 80 90 100
No. of students:6 15 26 41 58 77 87 93 97 100
Find the limits for central 50%
Find the co-efficient of variation.
A manufacturer of flashlight batteries took a sample of 13 batteries from a days production and used them continuously until they were drained. The number of hours they were used until failure were:
342 426 317 545 264 451 1049 631 512 266 492 562 298
Provide a box and whisker plot and then describe the shape.
The following data represents the age of 30 patients from a hospital :
17 8 22 19 7 14
13 21 28 17 29 22
20 17 14 16 19 13
18 11 34 17 11 15
11 20 25 32 21 12
Construct a histogram and frequency polygon for the age.
Also find the age group which contains maximum number of patients.
Calculate the standard deviation, variance and co-efficient of variation of frequency distribution.
The stem and leaf display below represents the number of vitamin supplements sold by a health food store in a sample of 16 days.
Stem leaves
9 9
0 0 2 3 5 6 7
0 3 4 5 6 8
1
Note: for this sample, the sum of the observations is 448, the sum of the squares is 13356 and the sum of the squared difference between each observation and the mean is 812.
List the five number summary of the number of vitamin supplements sold in this sample.
Calculate the coefficient of variation of the number of vitamin supplements sold in this sample.
The arithmetic mean and standard deviation of 20 items were calculated by a student as 20 cm and 5cm respectively. But while calculating an item 13 was misread as 30.find the correct mean and standard deviation.
The mean and the standard deviation of a sample of size 10 were found to be 9.5 and 2.5 respectively. Later on, an additional observation became available. This was 15, which is included in the original sample. Find the mean and the standard deviation of the 11 observations.
Mean and standard deviation of 200 items are found to be 60 and 20. If at the time of calculations two items were wrongly taken as 3 and 67 instead of 13 and 17, find the correct mean and standard deviation.
The combined mean and variance of the salary of 250 workers of city A and city B are 560 and 549 respectively. The mean and the variance of the salary of 100 workers of city A are 650 and 121 respectively. Find the variance of the salary in city B. Calculate the coefficient of variation of the combined set.
The mean of 100 items was 40 and the standard deviation 10. It was later discovered that two items were wrongly read as 30 and 70 instead of 3 and 27. Find the correct mean and standard deviation.
The means of two samples of sizes 50 and 100 respectively are 54.1 and 50.3 and the s.d. is 8 and 7. Find the mean and standard deviation of the sample obtained by combining the two samples. Also calculate the coefficient of variation of the combined set.
The first of the two samples has 100 items with mean 15 and s.d. 3. If the whole group has 250 items with mean 15.6 and standard deviation 13.44. Find the s.d. of the second sample.
The scores of two golfers for 10 rounds each are:
A: 58 59 60 54 65 66 52 75 69 52
B: 84 56 92 65 86 78 44 54 78 68
Find which golfer is more consistent player.
A student obtained the mean and S.D. of 100 observations as 40 and 5.1 respectively. It was later discovered that he had wrongly copied down an observation as 50 instead of 40. Calculate the corrected mean and S.D.
The following are distribution of marks in a certain examination.
Marks : below 10 below 20 : below 30 below 40 below 50
Fre. : 10 20 25 40 65
Calculate the mean, S.D, variance and co-efficient of variations.
An analysis of monthly wages paid to the workers in two firms A and B belonging to the same industry give the following results
Firm A Firm B
No. of workers: 600 700
Average monthly wage: Rs. 182 Rs. 178.5
Variance of distribution: 78 98
Which firm A or B has a larger bill?
In which firm A or B is there greater variability in individual wage?
The average electricity consumption and standard deviation of two sets of households are as follows.
Set ISet IIMean65 units72 unitsStandard deviation13 units18 unitsNumber of households5040Which set is more variable?
Calculate the coefficient of variation of the combined set.
PAGE
Measures of Dispersion
PAGE
PAGE 6
Measures of Dispersion Bal Krishan Khadka
Ace-BBA-III, Business Statistics
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