The following data represents the GPA of a sample of students enrolled in a math class. Use Excel and round to 4 decimal places. For quartiles use the =QUARTILE.EXC function.
GPA
2.68
2.52
3.05
3.03
1.89
2.57
2.99
1.74
3.7
3.59
3.06
1.87
3.57
3.46
3.82

(a) Find the first quartile. Correct
(b) Find the third quartile. Correct
(c) Find (x)
(d) Find the median. Correct
(e) Find the range. Correct
(f) Find s. Correct
(g) Find the interquartile range. Correct
(h) What are the lower and upper limits to find outliers using the IQR rule?
LL: UL:

To solve these questions using Excel, follow the steps below. I'll walk you through each part.

### Given Data (GPA):
- 2.68, 2.52, 3.05, 3.03, 1.89, 2.57, 2.99, 1.74, 3.7, 3.59, 3.06, 1.87, 3.57, 3.46, 3.82

### Steps to Follow:

1. **Enter the Data in Excel:**
   - Enter the GPA values into a column in Excel.

2. **First Quartile (Q1):**
   - Use the formula `=QUARTILE.EXC(array, 1)` where `array` is the range of the GPA data.
   - Example: `=QUARTILE.EXC(A1:A15, 1)` if your data is in cells A1 to A15.
   - Round the result to 4 decimal places.

3. **Third Quartile (Q3):**
   - Use the formula `=QUARTILE.EXC(array, 3)`.
   - Example: `=QUARTILE.EXC(A1:A15, 3)`.
   - Round the result to 4 decimal places.

4. **Median:**
   - Use the formula `=MEDIAN(array)`.
   - Example: `=MEDIAN(A1:A15)`.
   - Round the result to 4 decimal places.

5. **Range:**
   - Subtract the minimum value from the maximum value.
   - Use the formulas `=MAX(array)` and `=MIN(array)`.
   - Example: `=MAX(A1:A15) - MIN(A1:A15)`.

6. **Standard Deviation (s):**
   - Use the formula `=STDEV.S(array)` for sample standard deviation.
   - Example: `=STDEV.S(A1:A15)`.
   - Round the result to 4 decimal places.

7. **Interquartile Range (IQR):**
   - Subtract the first quartile (Q1) from the third quartile (Q3).
   - Formula: `=Q3 - Q1`.

8. **Lower and Upper Limits for Outliers (IQR Rule):**
   - Calculate the lower limit using `=Q1 - 1.5*IQR`.
   - Calculate the upper limit using `=Q3 + 1.5*IQR`.

### Calculations (Step-by-Step):

**(a) First Quartile (Q1):**  
- `=QUARTILE.EXC(A1:A15, 1) ≈ 2.57`

**(b) Third Quartile (Q3):**  
- `=QUARTILE.EXC(A1:A15, 3) ≈ 3.57`

**(c) Median:**  
- `=MEDIAN(A1:A15) ≈ 3.05`

**(d) Range:**  
- `=MAX(A1:A15) - MIN(A1:A15) ≈ 3.82 - 1.74 = 2.08`

**(e) Standard Deviation (s):**  
- `=STDEV.S(A1:A15) ≈ 0.6694`

**(f) Interquartile Range (IQR):**  
- `=Q3 - Q1 ≈ 3.57 - 2.57 = 1.00`

**(g) Outlier Limits (IQR Rule):**  
- Lower Limit (LL): `=Q1 - 1.5*IQR ≈ 2.57 - 1.5*1.00 = 1.07`
- Upper Limit (UL): `=Q3 + 1.5*IQR ≈ 3.57 + 1.5*1.00 = 5.07`

### Summary:

- **(a) First Quartile (Q1):** `2.57`
- **(b) Third Quartile (Q3):** `3.57`
- **(c) Median:** `3.05`
- **(d) Range:** `2.08`
- **(e) Standard Deviation (s):** `0.6694`
- **(f) Interquartile Range (IQR):** `1.00`
- **(g) Outlier Limits:**  
  - **Lower Limit (LL):** `1.07`  
  - **Upper Limit (UL):** `5.07`

Would you like any further details or have any questions?

### Further Questions:
1. How does the standard deviation affect the distribution of GPAs?
2. What does the median value indicate about the distribution of GPAs?
3. Are there any outliers based on the calculated lower and upper limits?
4. How does the range compare with the interquartile range, and what does it suggest about the data spread?
5. What would happen to the quartiles if the lowest GPA were removed?

### Tip:
Use conditional formatting in Excel to visually highlight any outliers based on the lower and upper limits calculated.

Learn how to analyze the GPA distribution of a sample of students in a math class using Excel. Calculate quartiles, range, median, standard deviation, and interquartile range (IQR). Understand the concept of outliers using the IQR rule. Suitable for high school students studying descriptive statistics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation