**u02a1** **–** **Central Tendency, Variability,** **Normal Curve,** **z****Scores, Probability, and Binomial Distribution**

Complete the following problems within this Word document (do not submit other files). Show your work for problem sets that require calculations. Ensure that 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).

**Problem** **Set 2.1**: **Median**

• **Criterion**: Calculate the median for a set of scores.• **Instruction**: Calculate the median of the provided data.• **Data**: Fifty employees were surveyed on their overall job satisfaction on a scale of 1 (not at all satisfied) to 10 (extremely satisfied). The results are tabulated in the table below. What is the median of this data set?

**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

*(Assessment* *continues on next page.)*

**Problem** **Set 2.2**: **Mode, Median, Mean, and Skew**

• **Criterion**: Calculate the mode, median, and mean for a set of scores.• **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. • **Instructions**: For the given data set, answer the following: a. What is the mode?b. What is the median?c. What is the mean? d. Are these scores normally distributed, positively skewed, or negatively skewed? e. Do you expect the mean to be higher or lower than the median?

**Problem** **Set 2.3**: **Range, Variance, and Standard Deviation**

• **Criterion**: Determine the range, variance, and standard deviation of a sample from raw scores.• **Data set**: A *sample* of students scored the following:

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.

• **Instructions**: For the given data set, answer the following: a. What is the range of scores?b. What is the variance in scores?c. What is the standard deviation in scores?

**Be sure to show your work.**

**Problem** **Set 2.4**: **Range, Variance, and Standard Deviation in SPSS**

• **Criterion**: Calculate measures of variability in SPSS from a group of raw scores.• **Instructions**: Complete the following steps: a. Enter the data from Problem Set 2.2 into SPSS using the variable name **Data**.b. In the Toolbar, click **Analyze**, select **Descriptive Statistics**, and then select **Descriptives.**c. Click **Data** and then click **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**.d. Click **OK** and copy and paste the descriptive statistics table below.e. Highlight the Range, Mean, and Standard Deviation. f. Answer: Does your Mean equal the Mean calculated in problem set 2.2?

*(Assessment* *continues on next page.)*

**Problem** **Set 2.5**: **Area and the Normal Curve**

• **Criterion**: Calculate *z* scores and find the area under a normal curve.• **Data**: The mean combined SAT score for a sample ofhigh school seniors is 1500 and the standard deviation is 250. • **Instructions**: Answer the following:a. What percentage of students scored below 1,000? b. What percentage of students scored above 1,750?

**Problem** **Set 2.6**: **Mutually Exclusive Outcomes**

• **Criterion**: Determine if events are mutually exclusive.• **Instruction**: Consider the following events. If the outcomes are mutually exclusive, type yes. If the outcomes are not mutually exclusive, type no.a. Turning right or turning left.b. Studying Spanish or studying Italian.c. Flipping heads on a coin or flipping tails on a coin.d. Drawing an eight from a deck of cards or drawing a king from a deck of cards.e. Riding a bike or wearing a hat.

**Problem Set 2.7**: **Probabilities: Dichotomous Events**

• **Criterion**: Calculate probability for a dichotomous event.• **Data**: Jane has flipped a coin 10 times, and each time it has landed on heads.• **Instruction**: Answer the following:o What is the probability that Jane’s eleventh flip will land on heads as well?

**Problem Set 2.8**: **z****Calcuations and the Unit Normal Table**

• **Criterion**: Calculate percentages based on *z* scores and the normal curve.• **Data**: For homes that 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.• **Instruction**: Using the Unit Normal Table, answer what percentage of homeowners:a. sold their home at the same point or earlier than the Carmichaels? b. sold their home at a later point than the Carmichaels? c. sold their home between 245 days and the average DOM?

*(Assessment* *continues on next page.)*

**Problem Set 2.9**: **Calculating** **z****Scores in SPSS**

• **Criterion**: Calculate *z* scores using SPSS.• **Data**: The following is a list of the number of goals scored over a 10-game soccer season:

2, 1, 5, 6, 0, 0, 3, 8, 1, 2.

**Instructions**: Complete the following steps:

a. Enter the data into SPSS using the variable name **Goals**.b. In the Toolbar, click **Analyze**, select **Descriptive Statistics**, and then select **Descriptives**.c. Click **Goals** and then click **Arrow** to send each over to the right side of the table. Check the box **save standardized values as variables**.d. Select **Options**, check the boxes **Mean** and **Standard Deviation**, and deselect all other boxes. Click **Continue**.e. Click **OK** and copy and paste the descriptive statistics table below.f. Go back to the **Data** **View** in SPSS. 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 this Word document.g. How many goals are closest to a *z* score of 0?

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