Question

Which of the following is/are true about average?

• A. Average of scores of a data should be a score of the given data
• B. Average of the scores of a data depends on the number of scores of the data
• C. Average can never be zero
• D. Average of scores of a data may vary when new scores are added

Answer 1

Answer: (B), (D)

The correct options are
B Average of the scores of a data depends on the number of scores of the data
D Average of scores of a data may vary when new scores are added

Average of scores of a data need not be a score of the data.
Consider the following scores: 1,2,3,2,3.
Average of the scores =$\frac{1+2+3+2+3}{5}=2.2$
2.2 is not a score of the given data

Average can take any value including zero depending on the scores of the given data.
Consider the following scores: -1,2,-3,2
Average of the scores = $\frac{(-1)+2+(-3)+2}{4}=0$
Average of the scores of the given data is 0.

Average of the scores of the data may vary when new scores are added.
Consider the following scores: 1,5,4,3,5
Average of the scores = $\frac{1+5+4+3+5}{5}=3.6$
Now, consider a new score 6 is added to the data.
Then, Average of the scores = $\frac{1+5+4+3+5+6}{6}$ = 4 $\ne$ 3.6 (old average)

Average of scores of a data depends on the number of scores of the data. Average of scores =$\frac{Sumofallscores}{Totalnumberofscores}$