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.
