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. 

(e) Find the range. 

(f) Find s. 

(g) Find the interquartile range. 

(h) What are the lower and upper limits to find outliers using the IQR rule? 

     LL: UL:

(i) Find s2. 




To solve these problems using Excel, here’s a step-by-step guide. We’ll go through each part and provide the necessary formulas and results rounded to four decimal places.

### 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 and Calculations:

**(a) First Quartile (Q1):**  
- **Excel Formula:** `=QUARTILE.EXC(A1:A15, 1)`
- **Result:** `2.5700`

**(b) Third Quartile (Q3):**  
- **Excel Formula:** `=QUARTILE.EXC(A1:A15, 3)`
- **Result:** `3.5700`

**(c) Find x:**  
- This might refer to an unknown value that is typically part of a different calculation, but since the exact nature of "x" is not specified, we would need additional context to answer this. If it means any other statistic, let me know.

**(d) Median:**  
- **Excel Formula:** `=MEDIAN(A1:A15)`
- **Result:** `3.0500`

**(e) Range:**  
- **Excel Formula:** `=MAX(A1:A15) - MIN(A1:A15)`
- **Result:** `3.82 - 1.74 = 2.0800`

**(f) Standard Deviation (s):**  
- **Excel Formula:** `=STDEV.S(A1:A15)`
- **Result:** `0.6694`

**(g) Interquartile Range (IQR):**  
- **Calculation:** `=Q3 - Q1`
- **Result:** `3.5700 - 2.5700 = 1.0000`

**(h) Outlier Limits (IQR Rule):**  
- **Lower Limit (LL):** `=Q1 - 1.5*IQR`
  - **Calculation:** `2.5700 - 1.5*1.0000 = 1.0700`
- **Upper Limit (UL):** `=Q3 + 1.5*IQR`
  - **Calculation:** `3.5700 + 1.5*1.0000 = 5.0700`

**(i) Variance (s²):**  
- **Excel Formula:** `=VAR.S(A1:A15)`
- **Result:** `0.4481`

### Summary of Results:

- **(a) First Quartile (Q1):** `2.5700`
- **(b) Third Quartile (Q3):** `3.5700`
- **(c) Find x:** (Additional context needed)
- **(d) Median:** `3.0500`
- **(e) Range:** `2.0800`
- **(f) Standard Deviation (s):** `0.6694`
- **(g) Interquartile Range (IQR):** `1.0000`
- **(h) Outlier Limits:**  
  - **Lower Limit (LL):** `1.0700`  
  - **Upper Limit (UL):** `5.0700`
- **(i) Variance (s²):** `0.4481`

Would you like any further details or clarification on any part?

### Further Questions:
1. How does the variance (s²) compare to the standard deviation (s)?
2. How would removing the lowest GPA affect the interquartile range?
3. Are there any outliers in the data based on the calculated limits?
4. What does the median value indicate about the distribution of GPAs?
5. How does the range of the data compare to the IQR, and what does this suggest about the data distribution?

### Tip:
In Excel, you can use the `=IF()` function combined with the outlier limits to automatically identify any outliers in your dataset.

Explore how to analyze GPA data using Excel. Learn to find quartiles, median, range, standard deviation, variance, and interquartile range (IQR) from a sample of student GPAs. Detailed step-by-step guide with Excel formulas and rounded results.

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