Question

The U.S. Department of Education reports that about 50% of all college students use a student loan to help cover college expenses (National Center for Educational Studies, January 2006). A sample of students who graduated with student loan debt is shown here. The data, in thousands of dollars, show typical amounts of debt upon graduation. 10.3 ​ 15.1 ​ 5.1 ​ 10.4 ​ 12.6 ​ 12.4 ​ 2 ​ 11.7 ​ 18.2 ​ 4.1 ​ a. For those students who use a student loan, what is the mean loan debt upon graduation ? (6) (in thousands) b. What is the sample variance and the sample standard deviation of loan debt (to 2 decimals)? Sample variance Sample standard deviation

Answer 1

a. The mean loan debt upon graduation for students who use a student loan is $10.19 thousand. b. The sample variance of loan debt is approximately 25.86, and the sample standard deviation is approximately 5.08.

Step-by-step explanation:

a. To find the mean loan debt upon graduation for those students who use a student loan, we need to calculate the average of the given data. We add up all the loan debt amounts and divide the sum by the total number of values.

b. To find the sample variance and sample standard deviation of loan debt, we need to calculate the variance and standard deviation of the given data. Sample variance is the average of the squared differences from the mean, and the sample standard deviation is the square root of the variance.

Step 1: Calculate the mean.

Mean loan debt = 10.19 thousand dollars (from part a).

Step 2: Calculate the squared differences from the mean.

Step 3: Calculate the sum of the squared differences.

Step 4: Calculate the sample variance.

Sample variance = Sum of squared differences / (n - 1) = 232.6959 / (10 - 1) = 25.8551 (rounded to 2 decimal places).

Step 5: Calculate the sample standard deviation.

Sample standard deviation = Square root of sample variance = Square root of 25.8551 ≈ 5.08 (rounded to 2 decimal places).