# Three Quantitative Problems: Frequency distributions

A. Develop a frequency distribution using classes of 12-14, 15-17, 18-20, 21-23, and 24-26.

B. Develop a relative frequency distribution and a percent frequency distribution using the classes in part (a)

Mendelsohn Media Research provided survey data on the annual amount of household purchases by families with an annual income of $75,000 or more (Money, 2001). Assume that the following data from a sample of 25 households show the dollars spent in the past year on books and magazines. Please see the excel attachment.

A. Construct a frequency distribution and relative frequency distribution for the data.

B. Provide a histogram. Comment on the shape of the distribution.

C. Comment on the annual spending on books and magazines for families in the sample.

The Nielsen Home Technology Report provided information about home technology and its usage by persons age 12 and older. The following data are the hours of personal computer usage during one week for a sample of 50 person. Please see excel attachment.

Summarize the data by constructive the following:

A. A frequency distribution (use a class width of 3 hours)

B. A relative frequency distribution

C. A histogram

D. An ogive

E. Comment on what the data indicate about personal computer usage at home.

These problem needs to be done in Excel what the instructions says.

See attached file for full problem description.

© BrainMass Inc. brainmass.com October 24, 2018, 8:54 pm ad1c9bdddfhttps://brainmass.com/statistics/frequency-distribution/three-quantitative-problems-frequency-distributions-111356

#### Solution Summary

The solution develops frequency distributions and analysis for them in three different questions.

Statistics Problems- Variety of Problems

1. A recent issue of Fortune Magazine reported that the following companies had the lowest sales

per employee among the Fortune 500 companies.

Company

Seagate Technology

SSMC

Russel

Maxxam

Dibrell Brothers

a. How many elements are in the above data set?

5

b. How many variables are in the above data set?

2 - Sales per Employee (1000s) and Sales Rank

c. How many observations are in the above data set?

5 - the same amount of elements that contain these observations. For example, the observation for the element Seagate Technology is $42.20; 285.

d. Name the scale of measurement for each of the variables.

Sales per Employee (1000s) = Interval

Sales Rank = Interval Scale

e. Name the variables and indicate whether they are qualitative or quantitative.

Sales per Employee (1000s) = Quantitative

Sales Rank - Quantitative

2.

Forty shoppers were asked if they preferred the weight of a can of soup to be 6 ounces, 8 ounces, or 10 ounces.

Below are their responses.

6 6 6 10 8 8 8 10 6 6

10 10 8 8 6 6 6 8 6 6

8 8 8 10 8 8 6 10 8 6

6 8 8 8 10 10 8 10 8 6

a. Construct a frequency distribution and graphically represent the frequency distribution.

Frequency Distribution:

Weight (in ounces) Frequency

6 14

8 17

10 9

Total 40

b. Construct a relative frequency distribution and graphically represent the relative frequency distribution.

Weight (in ounces) Frequency Relative Frequency % Frequency

6 14 0.35 35

8 17 0.43 42.5

10 9 0.23 22.5

Total 40 1 100

3.

A sample of 9 mothers was taken. The mothers were asked the age of their oldest child. You are given their responses below.

3 12 4 7 14 6 2 9 11

a. Compute the mean.

7.555555556

b. Compute the variance.

17.77777778

c. Compute the standard deviation.

4.216370214

d. Compute the coefficient of variation.

55.80489989

e. Determine the 25th percentile.

4

f. Determine the median.

7

g. Determine the 75th percentile.

11

h. Determine the range.

12

4.

The sales record of a real estate agency show the following sales over the past 200 days.

Number of Number

Houses Sold of Days

0 60

1 80

2 40

3 16

4 4

200

a. How many sample points are there?

5

b. Assign probabilities to the sample points and show their values.

60/200 = 0.3

80/200 = 0.4

40/200 = 0.2

16/200 = 0.08

4/200 = 0.02

1

c. What is the probability that the agency will not sell any houses in a given day?

60/200 = 0.3

d. What is the probability of selling at least 2 houses?

60/200 = 0.3

e. What is the probability of selling 1 or 2 houses?

80+40 = 120/200 = 0.6

f. What is the probability of selling less than 3 houses?

16+40+80+60 = 196/200 = 0.98

5.

Six viamin and three sugar tablets identical in appearance are in a box. One tablet is taken at random and given to person A.

A tablet is then selected and given to Person B.

What is the probability that n(S) = 9 P(A) = 6/9 =0.666667

n(A) = 6 P(B) = 3/9 = 0..33333

a. Person A was given a vitamin tablet? n(B) = 3

6/9 = 0.666666667

b. Person B was given a sugar tablet given that Person A was given a vitamin tablet?

3/8= 0.38

c. Neither was given vitamin tablets?

3/9= 0.333333333

d. Both were given vitamin tablets?

6/9 = 0.666666667

e. Exactly one person was given a vitamin tablet?

1 / 6 = 0.166666667

f. Person A was given a sugar tablet and Person B was given a vitamin tablet?

6.

The demand for a product varies from month to month. Based on the past year's data, the following probability distribution shows MNM

company's monthly demand.

x F(x) xf(s)

Unit Demand Probability

0 0.10 0(.10) = .00

1000 0.10 1000(.10) = 100

2000 0.30 2000(.30) = 600

3000 0.40 3000(.40) = 1200

4000 0.10 4000(.10) = 400

1.00 2300

a. Determine the expected number of units demanded per month.

2300

b. Each unit produced costs the company $8.00, and is sold for $10.00. How much will the company gain or lose in a month if they stock

the expected number of units dmanded, but sell 2000 units?

2300 x 8 18400 $20,000 - $18,400 = 1600 Loss

2300 x 10 23000

2000 x 8 16000

2000 x 10 20000

7.

a. Define the random variable in words.

A random variable is a numerical description of the outcome of an experiment. The particular numerical value of the random variable depends on the

outcome of the experiment. In this case we have a discrete random variable.

b. The mayor of Daisy City makes $2,250 a month. What percentage of Daisy City's residents has incomes that are more than the mayors?

x = 2250 2250-3000 =-750 / 500 = -1.5

μ = 3000 z = .0668

σ = 500 1-.0668 = 0.9332 93.32%

c. Individuals with incomes of less than $1,985 per month are exempt from city taxes. What percentage of residents is exempt from city taxes?

x = 1,985 1985-3000 = -1015 / 500 = -2.03

μ = 3000 z = .0212

σ = 500 1-.0212 = 0.9788 97.88%

d. What are the minimum and the maximum incomes of the middle 95% of the residents?

View Full Posting Details