Question Video: Recalling the Process for Estimating the Mean of Grouped Data | Nagwa Question Video: Recalling the Process for Estimating the Mean of Grouped Data | Nagwa

Question Video: Recalling the Process for Estimating the Mean of Grouped Data Mathematics • Second Year of Preparatory School

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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 × class frequency) ÷ sum of frequencies. [B] We calculate the upper limit of each class and then use the following rule: sum of (each upper limit × class frequency) ÷ sum of frequencies. [C] We calculate the midpoint of each class and then use the following rule: sum of (each midpoint × class frequency) ÷ sum of frequencies. [D] We calculate the midpoint of each class and then use the following rule: sum of (each midpoint × class frequency) ÷ sum of midpoints. [E] We calculate the lower limit of each class and then use the following rule: sum of (each lower limit × class frequency) ÷ sum of lower limits.

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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.

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