Question

For a Math 221 project, one group of students studied the ages of students on the BYU-Idaho campus. They collected data from a random sample of n = 100 students. The sample mean was 21.2 and the sample standard deviation was 2.61. An excerpt of their data is given below.

ID GENDER AGE
1 Female 21
2 Male 18
3 Male 12
4 Female 20
: : :
99 Male 25

The group notices an error in their data. The age of one of the males (ID=3) was entered incorrectly. He is actually 21 years old.

When the error is corrected, what will happen to the sample mean?


A)The mean will increase.
B)The mean will decrease.
C)The mean will stay the same.
D) It is not possible to determine this without the full data set.

Answer 1

When the age of a male student in the dataset is corrected from 12 to 21, the sum of the ages increases, and since the total number of students (n=100) remains constant, the sample mean will increase. Therefore, the correct answer is A) The mean will increase.

Step-by-step explanation:

The question deals with the impact of correcting an error in a dataset on the calculation of statistical measures, specifically the sample mean. The original dataset from a sample of students at BYU-Idaho included an age entry for a male student listed as 12 years old, which was recorded incorrectly. The actual age of the student is 21 years old. To understand what will happen to the sample mean when this error is corrected, we consider the formula for calculating the mean, which is the sum of all values divided by the number of values (n).

Initial mean calculation:
Mean = (Sum of ages including the incorrect age) / n

Corrected mean calculation:
Mean = (Sum of ages with correct age) / n

Since the incorrect age is 12 and the correct age is 21, substituting 12 with 21 increases the sum of ages. Consequently, the mean will increase because the numerator of the mean calculation is getting larger while the denominator remains the same (n=100).

Thus, when the error in the dataset concerning the male student's age is corrected, the correct option for what will happen to the sample mean is:
A) The mean will increase.