### Video Transcript

In order to estimate the mean from
given grouped data, which of the following is true? (A) We calculate the lower limit of
each class and then use the following rule: sum of each lower limit multiplied by
class frequency divided by sum of frequencies. (B) We calculate the upper limit of
each class and then use the following rule: sum of each upper limit multiplied by
class frequency divided by sum of frequencies. (C) We calculate the midpoint of
each class and then use the following rule: sum of each midpoint multiplied by class
frequency divided by sum of frequencies. (D) We calculate the midpoint of
each class and then use the following rule: sum of each midpoint multiplied by class
frequency divided by sum of midpoints. (E) We calculate the lower limit of
each class and then use the following rule: sum of each lower limit multiplied by
class frequency divided by sum of lower limits.

In this question, we’re asked to
recall the process for estimating the mean of grouped data. This means that data will be
presented in a frequency distribution and divided into classes. We won’t be given any of the exact
data values. But we will be told how many of the
values lie in each class.

In general, we find the mean of a
data set by dividing the sum of all the data values by how many values there
are. When we’re estimating the mean of a
frequency distribution, however, we can only estimate the sum of the data values due
to them being grouped. We first estimate the sum of the
values within each class by multiplying a value that is most representative of that
class by the class frequency.

We can see that this is what is
described in each of the five answer options. In each case, some value from each
class is multiplied by the class frequency. The question is, which value in a
class is most representative of that class?

Well, the answer to that is “the
midpoint of the class,” as it is the value exactly in the center of the class. And so we would expect that using
this value to represent each individual value in the class would have the least
error on average.

So we multiply each midpoint by the
frequency for that class to give an estimate of the sum of the values within that
class. Finding the sum of these products
for every class gives an estimate of the sum of all the data values.

Returning to the formula, we need
to divide this estimated sum by the number of values in the data set. That corresponds to the total
frequency, or the sum of all the class frequencies. Hence, we can deduce that option
(C) is the correct answer. To estimate the mean of grouped
data, we calculate the midpoint of each class and then use the following rule: the
sum of each midpoint multiplied by the class frequency divided by the sum of the
frequencies.