Question

The mean of the following data values is 36.
19, 23, 35, 41, 42

Answer 1

To find the mean of a set of data, we need to sum up all the values in the set and divide by the number of values.

Sum of the data values = 19 + 23 + 35 + 41 + 42 = 160

Number of data values = 5

Mean = Sum of data values / Number of data values = 160 / 5 = 32

However, we are given that the mean is 36. Since the calculated mean is lower than the given mean, it means that we are missing a value that is higher than the other values in the set.

Let's call this missing value x. Then, we have:

(19 + 23 + 35 + 41 + 42 + x) / 6 = 36

Multiplying both sides by 6, we get:

19 + 23 + 35 + 41 + 42 + x = 216

Simplifying the left-hand side, we get:

160 + x = 216

Subtracting 160 from both sides, we get:

x = 56

Therefore, the missing value is 56, and the complete data set is:

19, 23, 35, 41, 42, 56

Now, we can calculate the mean as:

Mean = (19 + 23 + 35 + 41 + 42 + 56) / 6 = 216 / 6 = 36

So, the mean of the data values is indeed 36.

Answer 2

32

Explanation:

To find the mean of a set of numbers, we add up all the numbers and then divide by the total number of values.

Adding up the values:

19 + 23 + 35 + 41 + 42 = 160

We have a total of 5 values, so we divide the sum by 5:

160 / 5 = 32

Therefore, the mean of the given data values is 32, not 36.