iCoachMath.com: Examples on Mean and Standard Deviation for Grouped Data - Data Description

Curriculum: Alaska Math Grade Level Expectations Click to change Curriculum

Topic: Data Description Click to change Topic

Lesson: M.A.6, B.1-3,6, D.1-2: Mean and Standard Deviation for Grouped Data Click to change Lesson

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e 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? e

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e 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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e 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?
e

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e 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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e 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.
e

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e 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. e

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e 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. e

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e 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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e The mean of the frequency distribution shown is 18.5. Find the value of t.

x	18	23	t	15	16
f	2	9	4	8	7

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e 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.
e

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e 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.
e

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e 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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e 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.
e

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e 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. e

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e 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. e

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e 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. e

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e 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. e

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e 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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e 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.
e

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e 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.
e

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e 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.
e

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e 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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e 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.
e

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e 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. e

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e 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.
e

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e 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.
e

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e 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. e

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