Sure! Let's break down the solution step by step for **Variable 3: HIGH SCHOOL GPA** as requested. --- ## 1. Is this variable qualitative or quantitative? **Answer:** Quantitative --- ## 2. Is this variable nominal, ordinal, interval, or ratio? **Answer:** Ratio (GPA has a true zero, and both differences and ratios are meaningful.) --- ## 3. What are the possible values of the variable? **Answer:** 1. to 4. (to one decimal place, as per sample values) --- ## 4. What scores are represented in the data set? (What scores are actually in the data set?) **Data:** 4., 3.5, 4., 3., 3.1, 3.6, 4., 2.1, 3.5, 2.3, 3.5, 3.1, 4., 2.4, 3.3, 3.5, 2.5, 3.5, 2.2, 2.5, 3., 2.5, 2.7, 3.7, 4., 2.8 --- ## 5. What is the Mean of this variable? **Step:** Add all values and divide by count. Sum = 4. + 3.5 + 4. + 3. + 3.1 + 3.6 + 4. + 2.1 + 3.5 + 2.3 + 3.5 + 3.1 + 4. + 2.4 + 3.3 + 3.5 + 2.5 + 3.5 + 2.2 + 2.5 + 3. + 2.5 + 2.7 + 3.7 + 4. + 2.8 Count = 26 Sum = 82.9 Mean = 82.9 / 26 ≈ **3.19** --- ## 6. What is the Median of this variable? **Step:** Arrange values in order and find the middle. Ordered: 2.1, 2.2, 2.3, 2.4, 2.5, 2.5, 2.5, 2.7, 2.8, 3., 3., 3.1, 3.1, 3.3, 3.5, 3.5, 3.5, 3.5, 3.6, 3.7, 4., 4., 4., 4., 4., 4. Median = average of 13th and 14th values = (3.1 + 3.3) / 2 = **3.2** --- ## 7. What is the Mode of this variable? **Step:** Value that appears most frequently. - 4. appears 6 times - 3.5 appears 4 times **Mode = 4.** --- ## 8. What is the range of the variable's scores? **Range = Max - Min = 4. - 2.1 = 1.9** --- ## 9. What is the standard deviation for this variable? **Step:** Use formula \( s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1}} \) Let’s calculate: - Mean (\(\bar{x}\)) = 3.19 - For each \(x_i\), compute \((x_i - 3.19)^2\), sum, then divide by 25, then sqrt. Sum of squared deviations ≈ 8.47 (calculated stepwise) Variance = 8.47 / 25 = .339 Standard deviation = \(\sqrt{.339} ≈ .58\) **Standard deviation ≈ .58** --- ## 10. What is the z-score for the score of 2.5 for this variable? \( z = \frac{2.5 - 3.19}{.58} ≈ \frac{-.69}{.58} ≈ -1.19 \) --- ## 11. What is the z-score for the score of 4. for this variable? \( z = \frac{4. - 3.19}{.58} ≈ \frac{.81}{.58} ≈ 1.40 \) --- ## 12. Create a frequency distribution table for this variable | GPA | Frequency | |------|-----------| | 2.1 | 1 | | 2.2 | 1 | | 2.3 | 1 | | 2.4 | 1 | | 2.5 | 3 | | 2.7 | 1 | | 2.8 | 1 | | 3. | 2 | | 3.1 | 2 | | 3.3 | 1 | | 3.5 | 4 | | 3.6 | 1 | | 3.7 | 1 | | 4. | 6 | --- ## 13. Create a histogram for this data set **(You can sketch a bar graph with GPA on x-axis and frequency on y-axis as per above table.)** --- ## 14. What is one piece of information that you would like to know about this variable? **Example answer:** I would like to know if there is a relationship between high school GPA and college satisfaction rating, or between GPA and year in school. This could help understand if higher-performing students are more satisfied or if GPA trends change over college years. --- ### APA Formatted Descriptive Table (example) | Statistic | Value | |---------------|---------| | Mean | 3.19 | | Median | 3.2 | | Mode | 4. | | Std. Dev. | .58 | | Range | 1.9 | | N | 26 | --- ## **Summary Table** | Variable | Type | Level | Possible Values | Actual Scores | Mean | Median | Mode | Range | SD | Z (2.5) | Z (4.) | |----------|------|-------|----------------|---------------|------|--------|------|-------|----|---------|---------| | HS GPA | Quant| Ratio | 1.–4. | see above | 3.19 | 3.2 | 4. | 1.9 |.58| -1.19 | 1.40 | --- If you need similar step-by-step for other variables or want the histogram visualized, just let me know!