Question

Find the value of X such that the data set has the given mean. 1, 5, 9, 10, 15, X; mean 8

Answer 1

To find the value of X that results in a mean of 8 for the given data set, the numbers in the set are summed excluding X, then divided by the total count, which leads us to calculating X as 8.

Step-by-step explanation:

To find the value of X such that the data set has a mean of 8, we first need to set up the equation for the mean. Since there are six numbers in the data set, we'll be dividing the sum of all numbers by 6. That gives us the following equation:

(1 + 5 + 9 + 10 + 15 + X) / 6 = 8.

Next, we solve for X:

1. Add up the numbers in the data set without X: 1 + 5 + 9 + 10 + 15 = 40.
2. Substitute the sum into the equation and solve for X: (40 + X) / 6 = 8.
3. Multiply both sides by 6 to get rid of the fraction: 40 + X = 48.
4. Finally, subtract 40 from both sides to find X: X = 48 - 40, so X = 8.

Thus, X must be 8 for the data set to have a mean of 8.