Final answer:
The mean of the given data set decreases when the number 3 is added, thus the correct answer is C. It decreases.
Step-by-step explanation:
When including the number 3 in the given data set of 34, 75, 26, 81, 65, 38, 49, the mean changes. To understand the impact of this inclusion, calculate the mean of the original data set and then calculate it again after adding the number 3. First, add up the original numbers: 34 + 75 + 26 + 81 + 65 + 38 + 49 = 368. The number of values in the set is 7, so you divide the sum by 7 to find the mean: 368 ÷ 7 = 52.57 (rounded to two decimal places).
Next, include the number 3 in the calculation. The new sum becomes 368 + 3 = 371. The number of values is now 8. Therefore, the new mean is 371 ÷ 8 = 46.38 (rounded to two decimal places).
Comparing the original mean of 52.57 to the new mean of 46.38 shows that the mean decreases when the number 3 is added to the data set. Hence, the correct answer to the question is C. It decreases.