Question Video: Finding and Interpreting the Mean of a Data Set | Nagwa Question Video: Finding and Interpreting the Mean of a Data Set | Nagwa

Question Video: Finding and Interpreting the Mean of a Data Set Mathematics • First Year of Preparatory School

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The table shows the total number of votes that each act received in a local talent show. Find the mean number of votes. Describe what the mean represents.

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Video Transcript

The table shows the total number of votes that each act received in a local talent show. Find the mean number of votes. Describe what the mean represents. (A) The average between the third and fourth terms. (B) The difference between the largest value and the smallest value in the list. (C) The number of votes that each act would have received if all the votes had been shared fairly among the acts.

We’re first asked to calculate the mean number of votes. The mean of a data set is calculated by finding the sum of all the values in the data set and dividing this by how many values there are. From the table, we can determine that there were six acts taking part in the talent show. So the number of data values is six. The sum of all the data values, which in this context is the total number of votes received, is 120. So, the mean number of votes is equal to 120 over six, which is 20.

The second part of the question asks us to describe what the mean represents. When we calculated the mean, we divided the total number of votes received by the number of acts taking part in the talent show. In other words, we shared the total number of votes equally between all the acts. So they all had the same number of votes. This is described in option (C), the number of votes that each act would have received if all the votes had been shared fairly among the acts.

So, we’ve found that the mean number of votes is 20. And this represents the number of votes each act would have received if the votes had been shared equally between them all.

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