Daniel has the following data: 18, 𝑚, 11, and 15. If the mean is 13, find the value of 𝑚.
We know that in order to calculate the mean, we need to divide the sum of values by the number of values. In order to calculate the sum of the values, we add 18, 𝑚, 11, and 15. 18 plus 11 plus 15 is equal to 44, so the sum of the values is 44 plus 𝑚. We know that there are four values in total. We are also told that the mean of these values is 13. We can substitute this into the formula or equation for the mean. 44 plus 𝑚 divided by four is equal to 13.
Multiplying both sides of this equation by four gives us 44 plus 𝑚 is equal to 52. Subtracting 44 from both sides of this equation gives us 𝑚 is equal to eight, as 52 minus 44 is eight. The value of 𝑚 in Daniel’s data is eight.
We could’ve approached this problem slightly differently by recalling that the sum of all our values is equal to the number of values multiplied by the mean. As four multiplied by 13 is 52, this would’ve taken us to the line 44 plus 𝑚 is equal to 52. Either way, we would end up with an answer of eight.