Video Transcript
The mean of the given data set is seven. Find the missing value 𝑥.
In this question, we are given all but one of the values in a data set and the mean of the data. We want to use this to find the missing value. To do this, we can start by recalling that the mean of a data set is the sum of all the values in the data set divided by the number of values in the data set.
We can see in the table that there are six values. So, our value of 𝑛 is six. We can then find an expression for the mean of the data set by adding all of the values in the data set together and dividing this sum by six as shown. Remember, we are told that the mean of this data set is seven. So, we have that seven is equal to nine plus six plus three plus eight plus five plus 𝑥 all divided by six.
We want to solve this equation for 𝑥. We can begin by evaluating the sum in the numerator to get that seven is equal to 31 plus 𝑥 all over six. Next, we multiply both sides of the equation by six to obtain 42 is equal to 31 plus 𝑥. Finally, we subtract 31 from both sides of the equation to get that 𝑥 is equal to 42 minus 31, which we can calculate is equal to 11.
