Question

Print-O-Matic printing company spends specific amounts on fixed costs every month. The costs of those fixed costs are in table #3.1.12.

a.) Find the mean and median. For median, list the numbers in order and show calculation. For mean, show calculation along with the sum.

b.) Find the mean and median with the bank charges removed. Describe what happened and why? Show calculation.

c.) Find the variance and standard deviation by creating a standard deviation table. Show work.

d.) Discuss why you used sample standard deviation or population standard deviation and why?

Monthly Charges	Monthly Cost ($)
Bank Charges	482
Cleaning	2208
Computer Expensive	2471
Lease Payments	2656
Postage	2117
Uniforms	2600

This ha been answered but my question is worded different then the others.

Answer 1

1) GIVEN:

The fixed cost for every month is given by,

Monthly Charges	Monthly Cost ($)
Bank Charges	482
Cleaning	2208
Computer Expensive	2471
Lease Payments	2656
Postage	2117
Uniforms	2600

Since the data is about the monthly cost spent by Print-O-Matic printing company for 6 purposes, the given data is treated as population of costs spent by the company because there are only totally 6 purposes for which the company spents and thus the population size is 6 and there are no other extra purposes. Thus the population size is fixed which is 6.

a) CALCULATION OF MEAN AND MEDIAN:

​MEAN:

The mean of a set of numbers, sometimes simply called the average, is the sum of the data divided by the total number of data.

Population size

Population mean

MEDIAN:

The median is the middle point of a number set, in which half the numbers are above the median and half are below. ​If the number of data points is odd, median is the middle value. But if the number of data points is​ even, the median is the mean of middle two values.

In the given dataset, the number of observations (Population size) is 6 which is even thus the median is the mean of middle two values.

First we have to rewrite the list of datapoints in ascending order:

Since population size is 6 (even), the median is the mean of middle two values,

Median

Since the mean value (2089) is less than the median (2439.5), the distribution of monthly cost is left (negatively) skewed and not symmetric.

b) MEAN AND MEDIAN WITH BANK CHARGES REMOVED:

​MEAN:

The mean of a set of numbers, sometimes simply called the average, is the sum of the data divided by the total number of data.

Population size

Population mean

MEDIAN:

The median is the middle point of a number set, in which half the numbers are above the median and half are below. ​If the number of data points is odd, median is the middle value. But if the number of data points is​ even, the median is the mean of middle two values.

In the given dataset, the number of observations (Population size) is 5 which is odd thus the median is the middle value.

First we have to rewrite the list of datapoints in ascending order:

Since population size is 5 (odd), the median is the middle value.

Median

Since the mean value (2410.4) is less than the median (2471), the distribution of monthly cost is left (negatively) skewed and not symmetric.

c) STANDARD DEVIATION AND VARIANCE:

Standard deviation is the measure of dispersion of a set of data from its mean.

The formula to calculate population standard deviation is given by,

We know that population mean

482	-1607	2582449
2208	119	14161
2471	382	145924
2656	567	321489
2117	28	784
2600	511	2611211

  

  

Thus the population standard deviation is .

VARIANCE:

Variance is the square of standard devaition.

Variance

Thus

  

Thus population variance ​ is .

d) I used population standard deviation because since the data is about the monthly cost spent by Print-O-Matic printing company for 6 fixed purposes, the given data is treated as population of costs spent by the company because there are only totally 6 fixed purposes it never change. As this represents the overall cost of the company and not the sample of costs spent. Thus the given data is treated as population and not sample. Thus population standard deviation is used.