Question Video: Identifying the Cumulative Frequency Graph for a Grouped Frequency Distribution | Nagwa Question Video: Identifying the Cumulative Frequency Graph for a Grouped Frequency Distribution | Nagwa

Question Video: Identifying the Cumulative Frequency Graph for a Grouped Frequency Distribution Mathematics • Second Year of Preparatory School

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A manufacturer samples the mass, in grams, of 30 pencils from their production line. Their masses are recorded in the table. No pencil has a mass greater than 60 g. Which cumulative frequency graph correctly shows this information? [A] Graph (A) [B] Graph (B) [C] Graph (C) [D] Graph (D) [E] Graph (E)

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Video Transcript

A manufacturer samples the mass, in grams, of 30 pencils from their production line. Their masses are recorded in the table. No pencil has a mass greater than 60 grams. Which cumulative frequency graph correctly shows this information? Is it graph (A), (B), (C), (D), or (E)?

In order to identify the correct graph, we need to calculate the cumulative frequencies for the values in the table. This will give us a running total for values that are less than a given point. The less than value that we will use will be the upper boundary of each class.

We begin by recognizing that the first group in the table represents masses that are 10 grams or greater but less than 20 grams. We can add the cumulative frequency row to our table, which will represent pencils with a mass of less than 20 grams, less than 30 grams, less than 40 grams, and so on. Since no pencil has a mass greater than 60 grams, the last element of the cumulative frequency row represents the number of pencils with masses less than 60 grams.

Recalling that cumulative frequency is the running total, we have values of three, nine, 20, 27, and 30. Note that we calculate these values by adding the frequency in that column to the previous cumulative frequency value. The final cumulative frequency will be the same as the total frequency. In this case, this will be the value 30, since 30 pencils were sampled.

When drawing or identifying the cumulative frequency graph in this context, we have the mass on the 𝑥-axis and cumulative frequency on the 𝑦-axis. The 𝑥-coordinate values will be the less than mass values or the upper boundaries of each class. This allows us to use a cumulative frequency curve to identify values that are less than any particular value. The coordinates that would be plotted can be given as 10, zero; 20, three; 30, nine; 40, 20; 50, 27; and 60, 30. As previously stated, the 𝑥-coordinate is the upper boundary of each group and the 𝑦-coordinate is the corresponding cumulative frequency. The graph that matches these coordinates is that of graph (B). And so this is the cumulative frequency graph for the given information.

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