Superior Essay Writers | Mean, Median, and Mode.

Mean, Median, and Mode.

2.1 A categorical variable has three categories, with the following frequencies of occurrence:

Category Frequency
A 13
B 28
C 9

a. Compute the percentage of values in each category.
b. What conclusions can you reach concerning the categories?

2.2 The following data represent the responses to two questions asked in a survey of 40 college students majoring in business: What is your gender? 1M=male; F=female2 and What is your major? (A=Accounting; C=Computer Information Systems; M=Marketing):

Gender: M M M F M F F M F M
Major: A C C M A C A A C C

Gender: F M M M M F F M F F
Major: A A A M C M A A A C

Gender: M M M M F M F F M M
Major: C C A A M M C A A A

Gender: F M M M M F M F M M
Major: C C A A A A C C A C

a. Tally the data into a contingency table where the two rows represent the gender categories and the three columns represent the academic major categories.
b. Construct contingency tables based on percentages of all 40 student responses, based on row percentages and based on column percentages.

3.2 The following set of data is from a sample of n=6:

7 4 9 7 3 12

a. Compute the mean, median, and mode.
b. Compute the range, variance, standard deviation, and coefficient of variation.
c. Compute the Z scores. Are there any outliers?
d. Describe the shape of the data set.

3.3 The following set of data is from a sample of n=7:

12 7 4 9 0 7 3

5.1 Given the following probability distributions:

Distribution A Distribution B

xi P(X=xi) xi P(X=xi)

0 0.50 0 0.05
1 0.20 1 0.10
2 0.15 2 0.15
3 0.10 3 0.20
4 0.05 4 0.50

a. Compute the expected value for each distribution.
b. Compute the standard deviation for each distribution.
c. Compare the results of distributions A and B.

5.2 The following table contains the probability distribution for the number of traffic accidents daily in a small town:

Number of Accidents Daily (X) P(X=xi)

0 0.10
1 0.20
2 0.45
3 0.15
4 0.05
5 0.05

a. Compute the mean number of accidents per day.
b. Compute the standard deviation.

5.3 Recently, a regional automobile dealership sent out fliers to perspective customers indicating that they had already won one of three different prizes: an automobile valued at $25,000, a $100 gas card, or a $5 Walmart shopping card. To claim his or her prize, a prospective customer needed to present the flier at the dealership’s showroom. The fine print on the back of the flier listed the probabilities of winning. The chance of winning the car was 1 out of 31,478, the chance of winning the gas card was 1 out of 31,478, and the chance of winning the shopping card was 31,476 out of 31,478.

a. How many fliers do you think the automobile dealership sent out?
b. Using your answer to (a) and the probabilities listed on the flier, what is the expected value of the prize won by a prospective customer receiving a flier?
c. Using your answer to (a) and the probabilities listed on the flier, what is the standard deviation of the value of the prize won by a prospective customer receiving a flier?
d. Do you think this is an effective promotion? Why or why not?

9.1 If you use a 0.05 level of significance in a two-tail hypothesis test, what decision will you make if ZSTAT = -0.76?

9.2 If you use a 0.05 level of significance in a two-tail hypothesis test, what decision will you make if ZSTAT = +2.21?

Sample Solution

Joined successions A succession (an) of genuine number is known as a focalized arrangements if a keeps an eye on a limited breaking point as n→∞. On the off chance that we say that (a) has a breaking point a∈ F if given any ε > 0, ε ∈ F, k∈ â„• | a – a | < ε n ≥ k In the event that a has a farthest point an, at that point we can compose it as liman = an or (a) → a. Cauchy Sequence A Cauchy succession is an arrangement in which numbers turn out to be nearer to each different as the grouping advances. On the off chance that we say that (an) is a Cauchy succession if given any ε > 0, ε ∈ F, k∈ â„• | a – am | < ε n,m ≥ k. Gary Sng Chee Hien, (2001). Limited sets, Upper Bounds, Least Upper Bounds A set is called limited if there is a sure feeling of limited size. A set R of genuine numbers is called limited of there is a genuine number Q with the end goal that Q ≥ r for all r in R. the number M is known as the upper bound of R. A set is limited in the event that it has both upper and lowe>

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