# Central Tendency, Variability, Normal Curve, Z Score

### Assessment Instructions

Answer the questions below, following the Submission Requirements as specified at the end of the assessment.

Assessment Concepts
Question Topic
Question 1 Ballpark and Exact Median
Question 2 Mode, Median, Mean, and Skew
Question 3 Range, Variance, and Standard Deviation
Question 4 SPSS: Range, Variance, and Standard Deviation
Question 5 Percent Area and the Normal Curve
Question 6 z Scores
Question 7 SPSS: Central Tendency and Z Scores
Question 8 Mutually Exclusive Outcomes
Question 9 Addition and Multiplication Theorems
Question 10 Probabilities: Dichotomous Events
Question 11 Probabilities: Using the Binomial Table

#### Question 1

Fifty employees were surveyed on their overall job satisfaction on a scale of 1 (not at all satisfied) to 10 (extremely satisfied). Using the below data, calculate the following:

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1. Start at the bottom of the table to determine the approximate median.
2. Use the median formula to determine the exact median.
Job Satisfaction
Job Satisfaction Score Frequency
10 2
9 8
8 13
7 10
6 7
5 4
4 2
3 2
2 1
1 1

#### Question 2

Given the following data set:

4, 2, 2, 2, 1, 1, 4, 5, 1, 3, 3, 3, 1, 2, 2, 2, 1, 4, 4, 3, 3, 2, 1, 2, 1.

Find the:

• Mode.
• Median (ballpark).
• Mean.

Are these scores normally distributed, positively skewed, or negatively skewed? Do you expect the mean to be higher or lower than the median?

#### Question 3

Consider the following set of scores taken from a sample of students:

3, 45, 4, 41, 14, 75, 40, 11, 9, 5, 21, 61, 48, 61, 29, 51, 44, 67, 39, 23, 45, 57, 60, 63, 62.

Find the following:

• Range.
• Variance.
• Standard deviation.

Be sure to show your work.

#### Question 4

Complete the following steps:

1. Open the SPSS file assessment2a.sav linked in the Resources under the Required Resources heading.
2. At the top of the screen, click on Analyze, select Descriptive Statistics, then select Descriptives.
3. Click on Score, then click on the arrow to send it over to the right side of the table. Select Options, check the boxes next to Variance and Range, and click Continue.
4. Click OK and copy and paste the descriptive statistics table to your Word document.

#### Question 5

Consider the mean combined SAT score for high school seniors is 1500, and the standard deviation is 250. Calculate the percentage of students who scored at the following levels:

• Below 1000.
• Above 1750.

#### Question 6

For homes sold in the past year, the average number of days on the market (DOM) was 266 days. During this time, DOM was normally distributed, with a standard deviation of 12 days. The Carmichaels sold their house in 245 days. Using the Area Under Normal Curve Table document linked in the Resources under the Required Resources heading, what percentage of homeowners:

• Sold their home at the same point or earlier than the Carmichaels?
• Sold their home at a later point than the Carmichaels?
• Sold their home between 245 days and the average DOM?

#### Question 7

Complete the following steps:

1. Open the SPSS file assessment2b.sav linked in the Resources under the Required Resources heading.
2. At the top of the screen, click on Analyze, select Descriptive Statistics, then select Descriptives.
3. Click on each variable (q1, q2, q3, q4), then click on the arrow to send each over to the right side of the table. Check the box next to save standardized values as variables.
4. Select Options, check the boxes next to Mean and Standard Deviation, and deselect all other boxes. Click on Continue.
5. Click OK and copy and paste the descriptive statistics table to your Word document.
6. Go back to the Variable View in SPSS, and you will see that the z scores have been added to the file. Paste a screenshot of the Variable View, showing the z scores, into your Word document.

#### Question 8

Consider the following events. If the outcomes are mutually exclusive, type “yes.” If the outcomes are not mutually exclusive, type “no.”

• Turning right or turning left.
• Studying Spanish and studying Italian.
• Flipping heads on a coin or flipping tails on a coin.
• Drawing an eight from a deck of cards or drawing a king from a deck of cards.
• Riding a bike or wearing a hat.

#### Question 9

Consider the following events. If the addition theorem applies, type “AT.” If the multiplication theorem applies, type “MT”:

• Drawing either a heart or a diamond from a deck of cards
• Either winning or losing a bet.
• Drawing (with replacement) a heart on three successive draws from a deck of cards.
• Rolling a six on three successive rolls of a die.

#### Question 10

Jane flips a coin 10 times, and each time it lands on heads. What is the probability that the 11th flip will land on heads as well?

#### Question 11

You have drawn nine cards. Using the Probability Binomial Table linked in the Resources under the Required Resources heading, calculate the following probabilities:

• Four or more cards will be black.
• Two or three cards will be black.
• Zero, one, or two cards will be black.
• Five cards will be black.

#### Submission Requirements

• Submit all answers in one Word document (do not submit multiple files).
• Show your work for questions that require calculations.
• Ensure your answer to each problem is clearly visible (you may want to highlight your answer or use a different font color to set it apart).