Statistics Question: Years to Earn Bachelor's Degree
Years to Earn Bachelor's Degree: Listed below are the lengths of time (in years) it took for a random sample of college students to earn bachelor's degrees (based on data from the National Center for Education Statistics). Based on these results, does it appear that it is common to earn a bachelor's degree in 4 years?
Years to Earn Bachelor's Degree 4 4 4 4 4 4 5 5 5 5 5 5 6 6 8 9 9 13 13 15
Define "common."
As indicated previously, if something happened 6 out of 20 times would you call that common?
To determine whether it is common to earn a bachelor's degree in 4 years based on the given data, we can calculate measures of central tendency such as the mean, median, and mode.
1. Mean: Add up all the numbers and divide by the number of data points.
- Total sum of the data: 4 + 4 + 4 + 4 + 4 + 4 + 5 + 5 + 5 + 5 + 5 + 5 + 6 + 6 + 8 + 9 + 9 + 13 + 13 + 15 = 135
- Number of data points: 20
- Mean = 135 / 20 = 6.75 years
2. Median: Arrange the data in ascending order and find the middle value.
- Arranged in ascending order: 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 8, 9, 9, 13, 13, 15
- The middle value is the median. In this case, with 20 data points, the median is the average of the 10th and 11th values.
- Median = (5 + 5) / 2 = 5 years
3. Mode: Check which value appears the most frequently in the data.
- In this case, the number 4 appears the most frequently, so it is the mode.
Based on the calculations, we can conclude the following:
- Mean: 6.75 years
- Median: 5 years
- Mode: 4 years
From these measures, we can see that the mean reflects a higher average time to earn a bachelor's degree due to some higher values in the data set. However, the median and mode both indicate that 4 years is a common time to earn a bachelor's degree. Therefore, based on this sample data, it appears that it is common to earn a bachelor's degree in 4 years.