The accompanying data set contains three numerical variables, x1, x2, and x3. a. How many observations have x1 values greater than 30? b. Sort the data by x1, x2, and then x3 all in ascending order. What are the x1, x2, and x3 values of the first observation after the data are sorted? c. Sort the data by x1 and x2 both in descending order. What are the x1, x2, and x3 values of the first observation after the data are sorted? d. How many missing values are there in x1, x2, and x3?
The Correct Answer and Explanation is:
To answer this question accurately, I would need the actual data set containing the numerical variables x1, x2, and x3. Since the data set was not provided, I will describe how to perform each task using software like Excel, Python, or R, and then I will show a sample solution using mock data.
Sample Data (10 observations)
| x1 | x2 | x3 |
|---|---|---|
| 25 | 15 | 10 |
| 32 | 18 | 9 |
| 29 | 22 | 14 |
| 45 | 25 | 20 |
| 30 | 17 | 12 |
| 28 | 21 | 11 |
| 33 | 20 | 13 |
| 19 | 15 | |
| 40 | 17 | |
| 27 | 16 |
(a) How many observations have x1 values greater than 30?
We examine each value in the x1 column:
- x1 values: 25, 32, 29, 45, 30, 28, 33, (missing), 40, 27
- Values greater than 30: 32, 45, 33, 40 → 4 observations
(b) Sort the data by x1, x2, then x3 in ascending order
After sorting:
- First complete observation (excluding missing x1):
x1 = 25, x2 = 15, x3 = 10
(c) Sort the data by x1 and x2 both in descending order
After sorting in descending order:
- First complete observation (excluding missing x1 or x2):
x1 = 45, x2 = 25, x3 = 20
(d) How many missing values are there in x1, x2, and x3?
Check for blanks:
- x1: 1 missing
- x2: 1 missing
- x3: 1 missing
Total: 3 missing values
Explanation
Data analysis often involves summarizing, sorting, and identifying missing values within a dataset. In this example, we explored three variables: x1, x2, and x3. The first task required identifying how many observations in the x1 column had values greater than 30. This is a straightforward filtering task. By reviewing each entry, we found four values exceeding 30: 32, 33, 40, and 45.
Next, we sorted the dataset by x1, x2, and x3 in ascending order. Sorting multiple columns helps when there are ties or closely related values. The ascending order starts from the smallest value and increases. The first observation after sorting reflects the smallest combination of x1, x2, and x3 values among all available data points.
For the third part, we sorted the data in descending order using x1 and x2. Sorting in descending order is useful when analyzing maximum values or identifying top performers. In this case, the largest x1 and x2 values determined the top row.
Lastly, missing data was evaluated. Data sets often have gaps due to errors in data entry or collection. Identifying and counting missing values helps assess data quality. Here, each column had one missing value, totaling three missing entries. This information can guide decisions on whether to exclude, impute, or further investigate these cases.
These types of operations are fundamental in data cleaning and exploration. Software tools like Excel (using filters and sort functions), Python (using pandas), or R (using dplyr) are commonly used to perform these tasks efficiently on larger datasets.
