Free Printable 03 Chebyshev's Theorem

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03 Chebyshev's Theorem

Total questions: 35

Worksheet time: 9hrs 45mins

Name

Class

Date

What is Chebyshev's Inequality?

P≥1-1/(k²)

P≥1+1/(k²)

P≤1-1/(k²)

P≤1+1/(k²)

What percent of the data in any data set lies within 7.5 standard deviations of the mean?

98.2%

86.7%

2.2%

13.3%

In any data set with 230 data points, what is the minimum number that must lie within 7 standard deviations of the mean?

226

204

153

In a data set with a mean of 24 and a standard deviation of 3, at least 75% of data points must lie between ________ and ________ [S.A.M.]

18 and 30

23.25 and 24.75

21 and 27

21.25 and 29.75

True or False: The percentages obtained by Chebyshev's Theorem are conservative lower estimates. The percent of data between any two boundaries is usually much more than the number given by the Theorem.

True

False

True or False: When finding the minimum number of data points between any two boundaries using Chebyshev's Theorem, if a decimal is obtained, you should round that decimal to the nearest integer.

True

False

The set of the weights of professional football players was found to have a mean of 275 lbs. with a standard deviation of 15 lbs. If there are a total of 1,650 pro football players in the US, what is the minimum number that weigh between 250 and 300 lbs.?

1,056

1,603

952

879

The mean age of a dinosaur fossil in a particular fossil bed is 85 million years. The standard deviation of the fossil ages from this bed is 1.5 million years. At least __________ of fossils in this bed are between 80 and 90 million years old.

91%

76.7%

99.3%

70%

Scientists measured the area claimed by each Bengal tiger in a certain jungle. The mean area claimed was 30 square miles with s=2.8 mi². At least 99% of the areas in this sample would have to be between _________________ mi²[S.A.M.]

2 and 58

27.2 and 32.8

20 and 40

17.2 and 42.8

10.

Review: Which of the following data displays is appropriate for univariate quantitative data?

Ogive

Bar graph

Scatter plot

Pie chart

11.

Review: In a survey, 15 out of 45 people were Steelers fans. If you were to make a pie chart out of the results of this survey, the slice for the Steelers would have an angle of...

120^o

133^o

150^o

145^o

12.

What does S.A.M. stand for in statistics?

Symmetric around the mean

Surface to air missile

Symmetric around the median

Symmetric around the mode

13.

What does the "k" in Chebyshev's Theorem represent?

Standard deviation

The number of standard deviations from the mean

Variance

The number of standard deviations from the median

14.

With each hop, how far does the bunny hop?

k units

One standard deviation

One unit

As far as it wants to

15.

What percent of the data in any data set must lie within 12 standard deviations of the mean?

99.3%

91.7%

11%

89%

16.

A data set has a mean of 50 and a standard deviation of 3.6. At least 80% of the data must lie between... [S.A.M.]

41.95 and 58.05

32 and 68

46.42 and 53.58

46.4 and 53.6

17.

In a data set with a mean of 25 and a standard deviation of 4.8, what is the minimum percent of the data that must lie between 20 and 30? [Round to the nearest percent.]

96%

88%

18.

400 books were selected at random from a library. If the mean length of books in this sample was 300 pages with s=20, what is the minimum number of books that must be between 200 and 400 pages?

384

396

375

214

19.

800 basketball players were selected at random. If their mean height was 78 in. with s=5, at least 650 of these players must have been between...

[S.A.M.]

66.45 and 89.55 in. tall.

70.05 and 85.95 in. tall.

51.35 and 104.65 in. tall.

72.25 and 83.75 in. tall

20.

In any data set, at least 60% of the data is within _______ standard deviations of the mean.

1.58

2.5

6.25

0.4

21.

What is the correct expression used to find the boundaries in a Chebyshev's Theorem problem?

mean ± k(s.d.)

k ± mean(s.d.)

(s.d) ± k(mean)

(s.d) ± k²(mean)

22.

A data set has 2,800 data points. What is the maximum number of data points in this set that could be more than six standard deviations away from the mean?

2,333

2,723

467

23.

A data set has a size of 200, a mean of 90 and a standard deviation of 5. What is the minimum number of data points that must lie between 80 and 100?

150

192

118

158

24.

Less than one out of a thousand data points in any set can be more than ______ standard deviations away from the mean

31.6

100

15.8

25.

Review: What is the median of the following data set:
{1, 3, 4, 4, 5, 6, 7}

26.

Review: Based on the dot plot, what is the skew of the data set represented?

Left

Right

Symmetric, but not Uniform

Uniform

27.

Review: Which type of set below would consist of nominal data?

Age

Height

Number of cousins

Favorite singer

28.

Review: What is the name of this data display?

Histogram

Time Series

Scatter Plot

Frequency Polygon

29.

Review: How many modes does the set represented by this data display have?

30.

A data set has 5,800 data points. At least 4,000 of these points must lie within how many standard deviations of the mean?

1.80

3.24

0.69

9.88

31.

A data set with a mean of 11 and s=0.6 has 724 data points. At least how many of these data points must be between 10 and 12?

464

528

290

430

32.

A data set with 800 data points has a mean of 33 and a standard deviation of 1.5. At least 700 of these data points must lie between what two boundaries, S.A.M.?

28.76 and 37.24

21 and 45

89.10 and 97.58

31.69 and 34.31

33.

$k=$

$\frac{\left|mean-boundary\right|}{st.\ dev.}$

$\frac{\left|mean+boundary\right|}{st.\ dev.}$

$\frac{\left|mean-\left(st.\ dev.\right)\right|}{boundary}$

$\frac{\left|mean+\left(st.\ dev.\right)\right|}{boundary}$

34.

True or False: Chebyshev's Theorem can only be used with boundaries that are symmetric around the mean

True

False

35.

True or False: It takes the same number of "hops" for the bunny to get to either boundary.

True

False

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03 Chebyshev's Theorem

Total questions: 35

Worksheet time: 9hrs 45mins

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