Question

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 median?


A) The median will increase.


B) The median will decrease.


C) The median will stay the same.


D) It is not possible to determine this without the full data set.

Answer 1

The correction of the student's age from 12 to 21 in the data set may or may not affect the sample median. Because we lack the full data set and do not know the original position of the incorrectly entered age relative to the median, we cannot determine what the impact on the median will be.

Step-by-step explanation:

When correcting an error in the data set related to the age of a BYU-Idaho student from 12 to 21 years old, we must consider the effect on the sample median. The median is the middle value of a data set when it is ordered from least to greatest.

In a sample of 100 students, the 50th and 51st values (assuming the data is ordered) determine the median. By increasing an age in the lower part of the data set (from 12 to 21), we are moving a value from below the median range to a value that could be near or above the median range. However, without the full data set, it is impossible to say definitively whether the sample median will increase, decrease, or stay the same.

If the originally incorrect age (12) were below the median, changing it to 21 could potentially raise the median if 21 is above the current median. If the incorrect age is within the lower 50% of the data but not at or below the 50th position in the ordered set, then correcting the age to 21 might increase the 51st value but will not affect the median.

Conversely, if the incorrect age is already above the median, correcting it will not affect the median at all. Since we do not know the exact position of the 12-year-old in the ordered data set relative to the median, option D) It is not possible to determine this without the full data set, is the accurate response to what will happen to the sample median upon making the correction.