Math project (Urgent)

Math 20-2 Statistical Reasoning Project

Part A:

This explanation will focus on how to do Part B of the project. Before you start Part A, look ahead at Part B to ensure your topic, research question and data would be suitable for the type of analysis done in Part B. For help with Part A, see pages 64-65, 122-123 and 170-171 of your text.

1. Collect your data. The data for this example is taken from Page 236 of your text book. Be sure to document your sources be it a website (Stats Canada) or other source

Media Focus Advertising

Computer Rescue

245000 362000 162000 112000 86000 96500 71000 96500 65000 63000 61000 62500 61000 59200 57500 59000 47400 56500 42500 55900 39500 55200 36200 53800 33400 53100 28500 52700 27300 52300

Part B:

1. Data analysis:

Measures of central tendency - (Mean, Median or Mode) – which one is best suited to your data? (Use the tips on page 312 as a guide)

For this example there are two outliers at the top of the pay scale for each company so it would be appropriate to either 1) use the median or 2) to use the mean after removing the outliers. We will look at both.

To calculate the median we find the middle term in the list using all 15 entries.

To calculate the mean we add up the 13 entries (having removed the outliers) and divide their sum by 13.

Media Focus Advertising Computer Rescue

Median = 57500 Median = 59000

Mean = 50485 Mean = 62785

Measures of Dispersion – (Range and Standard Deviation) – the range is ill-suited for this data due to the two big outliers (again refer to tips on page 312 as a guide). Standard deviation is calculated on the graphing calculator using lists. The calculator instructions are on the standard deviation page under content with a video as well to help step you through.

Because the outliers can affect the standard deviation so greatly, again we will only use the 13 measures to calculate standard deviation (leaving out the outliers).

Media Focus Advertising – Standard Deviation = 17 263

Computer Rescue – Standard Deviation = 14 758

Normal Distribution and z-scores

You may need to choose a value to compare within your data. For example, for this data we are going to choose a salary of $75000 to compare between the two companies. To do this comparison you would use z-scores (as shown below and using the tables on pages 580 & 581 of your textbook)

z = (x – mean)/standard deviation or 𝑧 = 𝑥−𝜇 𝜎

Media Focus Advertising 𝑧 = 75000−50485 17263

z =1.42 This z score means 92.22% of the people in

the company have salaries lower than this

Computer Rescue 𝑧 = 75000−62785 14758

z = 0.83 This z score means 79.67% of people in the

company have salaries lower than this

Margin of Error and Confidence Intervals

This type of data doesn’t relate as well to margin of error or confidence interval calculation as the results of a survey would. Therefore, we will choose a margin of error for our data such as 5% and calculate the confidence interval of our mean.

Margin of Error Chosen = 5%

Media Focus Advertising Confidence Interval = 17263 ± 5%

= 17263 ± 863

= 16400 to 18126

Computer Rescue Confidence Interval = 14758 ± 5%

= 14758 ± 738

= 14020 to 15496

Part C:

1. Discuss the appropriateness of your analysis and identify any controversial issues This is where you would discuss things such as taking out the outliers to have a more representative Mean and your choices for x in the z-score calculations and for the margin of error. Were there any controversial issues? Pages 390-391 and 438-439 of your text are an excellent aid. For example: The medians for each company were similar but for Media Focus Advertising the mean was much smaller with a higher standard deviation. This shows that the company has a lower average salary and that the salaries vary greater from that average. This is also shown in the z- score analysis because a salary of $75000 places the employee ahead of 92% of their co-workers compared to 79% with Computer Rescue.

2. Create a presentation You may create a Powerpoint, make a webpage, write a story, design an advertisement etc. to display your work.