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| f The average score of students in statistics examination is 90, with a variance of 4. The average score of students in algebra examination is 102, with a variance of 7. Which course is more variable in terms of scores? f |
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f The average age of technicians at B & T company is 26 years, with a standard deviation of 6 years. The average salary of the technicians is $31,000 with a standard deviation of $4000. Is the variation in the salary of technicians more than the variation in their age ?
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f The average score on a Geography final examination was 70, with a standard deviation of 5. The average score on an English final examination was 85 with a standard deviation of 8. Which class was more variable?
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f The average age of the accountants at Six Soft Technologies is 24 years, with a standard deviation of 4 years. The average salary of the accountants is $30,000 with a standard deviation of $2,500. Compare the variations of age and income.
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f The scores of 60 students of a class are shown in the frequency distribution.| Scores | Frequency | | 86 - 96 | 14 | | 97 - 107 | 7 | | 108 - 118 | 13 | | 119 - 129 | 10 | | 130 - 140 | 11 | | 141 - 151 | 5 |
Find the mean and the modal class of the data.
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| f The mean for the number of viewers of a sample of entertainment programs is 132, with a variance of 23. The mean for the number of advertisements of a sample of entertainment programs is 182, with a variance of 62. Compare the variations. f |
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f If X¯ is mean, s is standard deviation and x is a value in the data set, then
I. About 68% of the data lies in the interval X¯ - s < x < X¯ + s.
II. About 95% of the data lies in the interval X¯ - 2s < x < X¯ + 2s.
III . About 99% of the data lies in the interval X¯ - 3s < x < X¯ + 3s.
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f A survey was conducted in a city to find the number of people (in %) of different age groups who did not complete their high school. The results are as shown in the frequency distribution table.
| Age group | Percentage of people | | 25 - 34 | 12 | | 35 - 44 | 18 | | 45 - 54 | 23 | | 55 - 64 | 37 | | 65 - 74 | 43 |
Find the variance and standard deviation. f |
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f The average number of computer sales over a 2-month period is 86, with a variance of 36. The average of the commissions is $4,444 with a standard deviation of $888. Find the coefficient of variations of the two and state which is more variable.
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f The net worth (in millions of dollars) of 30 business units in a city are shown in the frequency distribution.| Net worth | Frequency | | 15 - 25 | 3 | | 26 - 36 | 10 | | 37 - 47 | 12 | | 48 - 58 | 5 |
Find the mean and the mode of the data and compare them. f |
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f A survey of 47 selected distributions showed these number of days that the load took to reach the shipment from the day it was ordered.| Days | Frequency | | 1 - 4 | 12 | | 5 - 8 | 8 | | 9 - 12 | 15 | | 13 - 16 | 5 | | 17 - 20 | 7 |
Find the mean and the modal class of the data. f |
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f The distribution of maximum load in short tons (1 short ton = 2000 lb) supported by certain cables produced by a company is shown. Find the mode and mean of the maximum load of the cables. Which is greater, mean or mode?| Maximum load | No. of cables | | 9.3 - 9.7 | 3 | | 9.8 - 10.2 | 5 | | 10.3 - 10.7 | 11 | | 10.8 - 11.2 | 16 | | 11.3 - 11.7 | 14 | | 11.8 - 12.2 | 7 | | 12.3 - 12.7 | 1 | | 12.8 - 13.2 | 3 |
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| f A test on knowledge of word refinishing has a mean of 53 and a standard deviation of 6. Smithy has been taking this test for the past six months and her score has a mean of 71 with a standard deviation of 9. Compare the two variabilities. f |
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f The mean of the frequency distribution shown is 18.5. Find the value of t.
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f Sixty eight randomly selected refrigerators were tested to determine their life span (in years). The relevant frequency distribution is as shown.
| Lifetime of refrigerators | Frequency | | 10.5 - 14.5 | 6 | | 14.5 - 18.5 | 12 | | 18.5 - 22.5 | 25 | | 22.5 - 26.5 | 17 | | 26.5 - 30.5 | 8 |
Find the variance and standard deviation.
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f Which of the following statement(s) is/are true?
I. Standard deviation is never negative.
II. Standard deviation is always positive.
III. Standard deviation is always zero.
IV. Standard deviation may be negative or positive or zero.
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f The number of people of different age groups visiting a recreation club in a town are as shown in the frequency distribution table.
| Age group | Number of people | | 10 - 15 | 9 | | 15 - 20 | 22 | | 20 - 25 | 35 | | 25 - 30 | 28 | | 30 - 35 | 31 | | 35 - 40 | 17 |
Find the mean of the data.
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f The table represents the percentage of house owners and corresponding ages (in years) of a municipal area in the year 2000. Find the variance and standard deviation.| Age | Percentage of house owners | | 15-24 | 17.9 | | 25-34 | 25.6 | | 35-44 | 16.2 | | 45-54 | 30.3 |
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f The weight (in grams) of a sample of 50 eggs are as shown in the frequency distribution table.
| Weight | Frequency | | 80 - 84 | 2 | | 85 - 89 | 6 | | 90 - 94 | 12 | | 95 - 99 | 14 | | 100 - 104 | 10 | | 105 - 109 | 5 | | 110 - 114 | 1 |
Find the variance and standard deviation.
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f The quiz scores of 50 students of a class is as shown in the frequency distribution.
| Quiz score | Frequency | | 0 - 2 | 6 | | 3 - 5 | 13 | | 6 - 8 | 9 | | 9 - 11 | 14 | | 12 - 14 | 8 |
Find the variance and standard deviation. f |
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f The net worth (in million dollars) of 60 export oriented quality leather manufacturing units in a large state are distributed as shown.| Net worth | Leather units | | 10 - 20 | 5 | | 21 - 31 | 10 | | 32 - 42 | 13 | | 43 - 53 | 7 | | 54 - 64 | 18 | | 65 - 75 | 7 |
Find the variance and standard deviation. f |
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f A field survey shows the lifetime (in years) of a particular model of a washing machine in the frequency distribution table.
| Lifetime of washing machines | Number of washing machines | | 0 - 2 | 5 | | 2 - 4 | 16 | | 4 - 6 | 13 | | 6 - 8 | 7 | | 8 - 10 | 5 | | 10 - 12 | 4 |
Find the variance and standard deviation. f |
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f The number of people of a residential colony and the years of their experience in driving are recorded in the table. Find the variance and standard deviation.| Experience | Number of people | | 0 - 2 | 23 | | 3 - 5 | 33 | | 6 - 8 | 63 | | 9 - 11 | 68 | | 12 - 14 | 19 | | 15 - 17 | 10 | | 18 - 20 | 1 |
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f The rate of fuel consumption (in miles per gallon) of 30 selected sports utility vehicles are shown in the frequency distribution table.
| Fuel consumption | Frequency | | 11.5 - 12.5 | 6 | | 12.5 - 13.5 | 1 | | 13.5 - 14.5 | 3 | | 14.5 - 15.5 | 6 | | 15.5 - 16.5 | 8 | | 16.5 - 17.5 | 2 | | 17.5 - 18.5 | 3 | | 18.5 - 19.5 | 1 |
Find the variance and standard deviation.
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f 80 randomly selected batteries were tested to determine their lifetime (in hours). The following frequency distribution was obtained.
| Lifetime of batteries | Frequency | | 63.5 - 74.5 | 10 | | 74.5 - 85.5 | 15 | | 85.5 - 96.5 | 22 | | 96.5 - 107.5 | 17 | | 107.5 - 118.5 | 11 | | 118.5 - 129.5 | 5 |
Find the variance and standard deviation of the data.
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f The blood urea nitrogen (in milligrams per deciliter - mg/dl) count of 20 randomly selected patients is shown in the frequency distribution table.
| Blood urea nitrogen | Frequency | | 11 - 13 | 3 | | 13 - 15 | 4 | | 15 - 17 | 3 | | 17 - 19 | 5 | | 19 - 21 | 5 |
Find the variance and standard deviation.
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f In a class of 20 students, this distribution of quiz scores was recorded. Find the standard deviation.| Score | Number of students | | 5.5 - 10.5 | 1 | | 10.5 - 15.5 | 2 | | 15.5 - 20.5 | 3 | | 20.5 - 25.5 | 5 | | 25.5 - 30.5 | 4 | | 30.5 - 35.5 | 3 | | 35.5 - 40.5 | 2 |
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