Mathematics – Statistics HOMEWORK 8 PSY

ANSWER

Question 1

How many players have values that are above the mean in this dataset?

To find this, we need to first calculate the mean and standard deviation of the field goal percentages from the given data:

• Mean (μ): Sum of all percentages / Number of players
• Standard Deviation (σ): A measure of the amount of variation or dispersion of a set of values.

Given data (field goal percentages):

• Jimmy Butler: 53.9
• Bam Adebayo: 54
• Tyler Herro: 43.9
• Max Strus: 41
• Kyle Lowry: 40.4
• Victor Oladipo: 39.7
• Caleb Martin: 46.3
• Gabe Vincent: 40.2
• Kevin Love: 38.8
• Cody Zeller: 62.7
• Duncan Robinson: 37.1
• Dewayne Dedmon: 49.6
• Nikola Jovic: 40.6
• Jamal Cain: 56.1
• Omer Yurtseven: 59.3
• Haywood Highsmith: 43.1
• Udonis Haslem: 34.5
• Jamaree Bouyea: 46.2
• Orlando Robinson: 52.8
• Dru Smith: 35.7

Calculating mean (μ): μ=53.9+54+43.9+41+40.4+39.7+46.3+40.2+38.8+62.7+37.1+49.6+40.6+56.1+59.3+43.1+34.5+46.2+52.8+35.720\mu = \frac{53.9 + 54 + 43.9 + 41 + 40.4 + 39.7 + 46.3 + 40.2 + 38.8 + 62.7 + 37.1 + 49.6 + 40.6 + 56.1 + 59.3 + 43.1 + 34.5 + 46.2 + 52.8 + 35.7}{20}μ=2053.9+54+43.9+41+40.4+39.7+46.3+40.2+38.8+62.7+37.1+49.6+40.6+56.1+59.3+43.1+34.5+46.2+52.8+35.7​ μ=835.120\mu = \frac{835.1}{20}μ=20835.1​ $\mu =41.755$

Calculating standard deviation (σ): Using the formula for standard deviation: σ=∑(Xiμ)2N\sigma = \sqrt{\frac{\sum (X_i – \mu)^2}{N}}σ=N∑(Xi​−μ)2​​

Let’s calculate step by step:

1. Calculate each deviation from the mean: $(53.9-41.755),(54-41.755),\dots ,(35.7-41.755)$
2. Square each deviation: (53.9−41.755)2,(54−41.755)2,…,(35.7−41.755)2(53.9 – 41.755)^2, (54 – 41.755)^2, \ldots, (35.7 – 41.755)^2(53.9−41.755)2,(54−41.755)2,…,(35.7−41.755)2
3. Sum up all squared deviations.
4. Divide by the number of data points.
5. Take the square root to find the standard deviation.

After calculating, assume you have a mean (μ) of 58

QUESTION

Individual HW 8 – Z Scores Summer 24 Started: Jun 17 at 7:48pm

Quiz Instructions

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Question 1 0.5 pts

This assignment is related to your Chapter 8 (Salkind) material.

Okay, you guessed it! More Miami Heat data! I know you might be getting a little tired of basketball data, and I understand, but stick with it! The reason I’m using the same dataset over and over again is so that you can see how we can use different types of statistical analyses to answer different types of questions.

Do you remember the mean and standard deviation for the dataset for the Miami Heat (you calculated them for assignment 6)? Great! You’ll need it for this assignment so you’ll have to go back to previous assignments to get those values (or you can calculate them again if you did not save your answers).

Miami Heat Player Name Field Goal %

Jimmy Butler 53.9

Bam Adebayo 54

Tyler Herro 43.9

Max Strus 41

Kyle Lowry 40.4

Victor Oladipo 39.7

Caleb Martin 46.3

Gabe Vincent 40.2

Kevin Love 38.8

Cody Zeller 62.7

Duncan Robinson 37.1

Dewayne Dedmon 49.6

Nikola Jovic 40.6

Jamal Cain 56.1

Omer Yurtseven 59.3

Haywood Highsmith 43.1

Udonis Haslem 34.5

Jamaree Bouyea 46.2

Orlando Robinson 52.8

Dru Smith 35.7

How many players have values that are above the mean in this dataset?

8

6/17/24, 10:31 PM Quiz: Individual HW 8 – Z Scores Summer 24

https://fiu.instructure.com/courses/201412/quizzes/1187542/take 1/5

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Question 2 0.5 pts

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Question 3 0.5 pts

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Question 4 0.5 pts

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Question 5 0.5 pts

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Question 6 0.5 pts

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Question 7 0.5 pts

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12

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9

How players have values that are below the mean?

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Calculate the z-score for Bam Adebayo. Round your answer to three decimal places. (you should also round the mean and standard deviation out three decimal places in your calculation to avoid rounding error).

Calculate the z-score for Jimmy Butler. Round your answer to three decimal places. (you should also round the mean and standard deviation out three decimal places in your calculation to avoid rounding error).

Calculate the z-score for Haywood Highsmith. Round your answer to three decimal places. (you should also round the mean and standard deviation out three decimal places in your calculation to avoid rounding error).

Calculate the z-score for Dru Smith. Round your answer to three decimal places. (you should also round the mean and standard deviation out three decimal places in your calculation to avoid rounding error).

Calculate the z-score for Tyler Herro. Round your answer to three decimal places. (you should also round the mean and standard deviation out three decimal places in your calculation to avoid rounding error).

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Question 8 0.5 pts

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Question 9 2 pts

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Question 10 2 pts

Calculate the z-score for Jamal Cain. Round your answer to three decimal places. (you should also round the mean and standard deviation out three decimal places in your calculation to avoid rounding error).

If you randomly select a professional basketball player, what is the probability that the player’s field goal percentage for the season is between Tyler Herro and Cody Zeller?

To answer this question you need to use the table in the appendix of the text to figure out the area between those two scores on the normal curve. Show your work on this. To get full credit, you must demonstrate all calculations, values you used from the appendix, and steps you took to get your answer (that is, your answer must include the z score, the area under the curve that you found in the appendix, and how you came to your final answer).

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If you randomly select an NBA player from the whole population, what percentage of the time would the player’s field goal percentage for the season be lower than Duncan Robinson?

To answer this question you need to use the table in the appendix of the text to figure out the area below this score. Show your work on this. To get full credit, you must demonstrate all calculations, values you used from the appendix, and steps you took to get your answer (that is, your answer must include the z score, the area under the curve that you found in the appendix, and how you came to your final answer).

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Question 11 2 pts

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You and your friend are engaging in a classic sports argument: which famous athlete is better at their respective sport? In other words, we’re going to explore the question: in the year 2023, was Jimmy Butler better at basketball than Travis Kelce (Tight End for Kansas City) was at football? Because we’re comparing to totally different sports with different statistics, in order to answer this question, we need to look at standardized scores (z-scores).

For Travis Kelce, we’ll look at Yards Per Catch (or Yards Per Reception), which shows the average number of yards a receiver gains every time they catch the football (how far do they take the ball each time they catch it?). It’s a simple but effective metric for evaluating the effectiveness and productivity of a Tight End.

In the 2023 season, Travis Kelcy had an average of 10.6 yards per catch. The total NFL average for tight ends that year was 9.77 with a standard deviation of 2.49.

Using this information tell me, who was better at their respective sport: Jimmy Butler or Travis Kelce?

In your answer include the following information:

a. The z scores for Kelce’s yards per catch and Jimmy Butler’s field goal percentage? b. A comparison of the two z scores and an explanation of your conclusion, based on those z-scores. What is your final

conclusion: who is better, relative to others in their respective sports? Why? c. Is this a fair comparison? Why or why not?

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Wait! Before you submit your answer, please save your response and work for the last question on this assignment. You need it for your discussion post and you will not be able to go back and view your answer before you do your discussion post.

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