Which data set has a mean of 8?1, 2, 4, 14, 161, 2, 4, 8, 102, 4, 8, 10, 162, 2, 4, 10, 16

To determine which data set has a mean of 8, we need to calculate the mean (average) for each data set. The mean is calculated by summing all the numbers in the data set and then dividing by the number of elements in the data set.

Let's calculate the mean for each data set step by step:

Data Set 1: 1, 2, 4, 14, 16

1. Sum of the numbers: $1 + 2 + 4 + 14 + 16 = 37$
2. Number of elements: 5
3. Mean: $\frac{37}{5} = 7.4$

Data Set 2: 1, 2, 4, 8, 10

1. Sum of the numbers: $1 + 2 + 4 + 8 + 10 = 25$
2. Number of elements: 5
3. Mean: $\frac{25}{5} = 5$

Data Set 3: 2, 4, 8, 10, 16

1. Sum of the numbers: $2 + 4 + 8 + 10 + 16 = 40$
2. Number of elements: 5
3. Mean: $\frac{40}{5} = 8$

Data Set 4: 2, 2, 4, 10, 16

1. Sum of the numbers: $2 + 2 + 4 + 10 + 16 = 34$
2. Number of elements: 5
3. Mean: $\frac{34}{5} = 6.8$

From the calculations above, we can see that the data set with a mean of 8 is:

Data Set 3: 2, 4, 8, 10, 16