UGC NET Questions (Paper – 1)

This option is correct because the arithmetic mean of two numbers is obtained by adding them and dividing by 2. Here, (10 + 20) ÷ 2 = 30 ÷ 2 = 15. This value lies exactly midway between 10 and 20. Therefore, the arithmetic mean is 15.

Option A:
Taking 10 as the mean would ignore the contribution of the larger number 20. The average must be between the two numbers and balanced by both. Since 10 is at the lower end, it cannot be the mean of 10 and 20.

Option B:
A value of 12 is between 10 and 20 but does not satisfy the mean formula. Using (10 + 20) ÷ 2 does not produce 12. Therefore, this number does not represent the correct arithmetic mean.

Option C:
20 is the larger of the two numbers and would be the mean only if both numbers were 20. Because the other number is 10, the mean must lie between 10 and 20, not at the greater endpoint. Thus, 20 is incorrect.

Option D:
The average 15 comes directly from the formula for mean and is equidistant from 10 and 20. It balances the two values, which is the key idea of an arithmetic mean. Hence, this option correctly answers the question.

To find the arithmetic mean, we add all the numbers and divide by how many numbers there are. Here, 4 + 6 + 8 + 10 = 28 and there are 4 observations. Dividing 28 by 4 gives 7. Therefore, the arithmetic mean of the given data set is 7.

Option A:
Option A is correct because it follows directly from the formula mean = sum of observations ÷ number of observations. The computation 28 ÷ 4 is straightforward and yields 7 exactly. In aptitude tests, performing such calculations accurately and quickly is crucial to managing time. Thus, 7 correctly represents the central value of the data.

Option B:
If we choose 8, we would be assuming that the average is equal to one of the larger values in the set, but the computation shows otherwise. Although 8 is close to the centre of the range, it does not equal the exact mean 7. Therefore, option B overestimates the average value.

Option C:
A mean of 6 would require that the total sum be 24, because 24 ÷ 4 = 6, but the actual sum is 28. This indicates that 6 is too low compared to the true average. Hence, this option does not match the correct calculation.

Option D:
A mean of 9 would imply a total sum of 36 for four values, which is much higher than the actual sum. Since the numbers lie between 4 and 10, an average as high as 9 is not consistent with the contributions of the smaller values. Therefore, this option is incorrect.