# Short answer questions in Statistics

1 What is a mean? A median? A mode?

2 What is a frequency distribution?

3 What is a normal distribution?

4 What is the approximate probability that a data point will fall within one standard deviation of the mean of a normally distributed data set?

5 How does one begin to use Excel (or other comparable software) to calculate basic statistics on a set of input data?

6 How does one use Excel (or other comparable software) to calculate and display a scatter diagram?

7 What is linear regression? What is the difference between simple regression analysis and multiple regression analysis?

8 What is the most important concept in regression analysis?

9 What are the limitations of regression analysis?

10 What is linear programming? What are the two major types of linear programming problems?

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#### Solution Preview

Please see attached file

1 What is a mean? A median? A mode?

"The mean is the average value of all the data in a data set.

The median is the value that has exactly half the data above it and half below it.

The mode is the value that occurs most frequently in the data set.

"

"The mean of a numeric variable is calculated by adding the values of all observations in a data set and then dividing that sum by the number of observations in the set.

Mean = sum of all the observation values ÷ number of observations

"

"If observations of a variable are ordered by value, the median value corresponds to the middle observation in that ordered list. The median value corresponds to a cumulative percentage of 50% (i.e., 50% of the values are below the median and 50% of the values are above the median).

The position of the median is (n+1)/2 Th value where n is the number of values in a set of data. In order to calculate the median, the data must be ranked (sorted in ascending order) first. The median is the number in the middle.

Median = the middle value of a set of data.

If the number of observations is odd, the median fits perfectly.

If the number of observations is even, one needs to find the midpoint between the numbers on either side of the median position.

"

"In a set of data, the mode is the most frequently observed data value. There may be no mode if no value appears more than any other. There may also be two modes (bimodal), three modes (trimodal), or four or more modes (multimodal).

Mode = the most frequently observed data value

"

2 What is a frequency distribution?

"A frequency distribution is a tabular arrangement of data where the data is grouped into different intervals, and then the number of observations that belong to each interval is determined. Data that is presented in this manner are known as grouped data.

"

3 What is a normal distribution?

"A normal distribution is a ...

#### Solution Summary

Answers short answer questions in statistics.

21 prob/stats multiple choice questions

Express the indicated degree of likelihood as a probability value.

1)

"You have a 50-50 chance of choosing the correct answer."

1)

_______

A)

50

B)

0.50

C)

0.9

D)

0.25

2)

"It will definitely turn dark tonight."

2)

_______

A)

0.67

B)

0.5

C)

0.30

D)

1

Answer the question.

3)

Which of the following cannot be a probability?

3)

_______

A)

0

B)

1

C)

-1

D)

From the information provided, create the sample space of possible outcomes.

4)

Flip a coin twice.

4)

_______

A)

HT TH

B)

HH HT TH TT

C)

HH TT HT HT

D)

HH HT TT

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

5)

On an exam on probability concepts, Sue had an answer of for one problem. Explain how she knew that this result was incorrect.

5)

_____________

6)

Discuss the range of possible values for probabilities. Give examples to support each.

6)

_____________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Determine whether the events are mutually exclusive.

7)

Draw one ball colored red from a bag.

Draw one ball colored blue from the same bag.

7)

_______

A)

Yes

B)

No

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

8)

Consider the following formulas: and

Given the same values for n and r in each formula, which is the smaller value, P or C? How does this relate to the concept of counting the number of outcomes based on whether or not order is a criterion?

8)

_____________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find the indicated probability.

9)

The table below describes the smoking habits of a group of asthma sufferers.

If one of the 1073 people is randomly selected, find the probability that the person is a man or a heavy smoker.

9)

_______

A)

0.614

B)

0.487

C)

0.545

D)

0.580

10)

A 6-sided die is rolled. Find P(3 or 5).

10)

______

A)

B)

C)

D)

2

Is Event B dependent or independent of Event A?

11)

A: A Chicagoan visits New York on vacation.

B: He visits Central Park.

11)

______

A)

Independent

B)

Dependent

Find the indicated probability.

12)

You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that both cards are black.

12)

______

A)

B)

C)

D)

Evaluate the expression.

13)

13)

______

A)

1

B)

5

C)

24

D)

120

14)

14)

______

A)

45

B)

80,640

C)

40,320

D)

5

Solve the problem.

15)

How many ways can an IRS auditor select 4 of 10 tax returns for an audit?

15)

______

A)

10,000

B)

5040

C)

210

D)

24

16)

There are 7 members on a board of directors. If they must elect a chairperson, a secretary, and a treasurer, how many different slates of candidates are possible?

16)

______

A)

35

B)

210

C)

5040

D)

343

17)

In a certain lottery, five different numbers between 1 and 36 inclusive are drawn. These are the winning numbers. To win the lottery, a person must select the correct 5 numbers in the same order in which they were drawn. What is the probability of winning?

17)

______

A)

B)

C)

D)

Identify the given random variable as being discrete or continuous.

18)

The number of freshmen in the required course, English 101

18)

______

A)

Discrete

B)

Continuous

19)

The height of a randomly selected student

19)

______

A)

Discrete

B)

Continuous

Find the mean of the given probability distribution.

20)

20)

______

A)

1.74

B)

1.45

C)

1.64

D)

1.55

21)

A police department reports that the probabilities that 0, 1, 2, and 3 burglaries will be reported in a given day are 0.50, 0.38, 0.11, and 0.01, respectively.

21)

______

A)

1.50

B)

0.25

C)

1.13

D)

0.63

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