Question

Here is a set of data 2.4, 1.6, 3.2, 0.3, 1.5. Calculate the mean, then increase it by 10, and finally double each new number. What is the sum of the doubled values?

a. 29.8
b. 28.6
c. 31.4
d. 30.2

Answer 1

After calculating the mean of the original data set, increasing it by 10, and then doubling each new number, the sum of the doubled values is 118.0, corresponding to option A.

Step-by-step explanation:

To calculate the mean of the data set 2.4, 1.6, 3.2, 0.3, 1.5, first we must add all the numbers together:

2.4 + 1.6 + 3.2 + 0.3 + 1.5 = 9.0

Next, we divide this sum by the number of values in the set, which is 5:

9.0 ÷ 5 = 1.8

The mean of the data set is 1.8. Now, we increase this mean by 10:

1.8 + 10 = 11.8

Then we double each number in the original data set after adding 10 to each:

(2.4 + 10) × 2 = 24.8,
(1.6 + 10) × 2 = 23.2,
(3.2 + 10) × 2 = 26.4,
(0.3 + 10) × 2 = 20.6,
(1.5 + 10) × 2 = 23.0

Finally, we sum these doubled values together to get:

24.8 + 23.2 + 26.4 + 20.6 + 23.0 = 118.0

Therefore, the correct answer is option A, which is 118.0.