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Question Video: Using a Cumulative Frequency Graph to Estimate the Frequency of Values Mathematics • 9th Grade

Mason took a sample of 100 balls from a box. He weighed each ball and recorded its weight in the table. He used the data to draw the cumulative frequency graph shown on the grid. Estimate how many balls had a weight of less than 80 g. Estimate how many balls had a weight of 130 g or more.

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Video Transcript

Mason took a sample of 100 balls from a box. He weighed each ball and recorded its weight in the table. He used the data to draw the cumulative frequency graph shown on the grid. Estimate how many balls had a weight of less than 80 grams. Estimate how many balls had a weight of 130 grams or more.

Cumulative frequency is the sum of all the previous frequencies up to the current point. It is often referred to as the running total of frequencies. The given graph shows the cumulative frequency of the weights of 100 balls. We can see from the graph that the highest cumulative frequency is 100. Any point on the cumulative frequency graph indicates the total number of balls that are less than the given weight.

In order to find an estimate for the number of balls that are less than 80 grams, we can draw a vertical line from 80 on the 𝑥-axis until it meets the curve. We then draw a horizontal line from this point to the 𝑦-axis to allow us to read the corresponding 𝑦-value, the cumulative frequency. Observing that each minor grid line on the 𝑦-axis represents a frequency of two, we can give the answer to the first part of this question. The number of balls less than 80 grams can be estimated as 26 balls.

Although each value on the cumulative frequency curve represents frequencies that are less than a particular value, we can still use the curve to find the values for greater than or equal to values. To estimate the number of balls that are 130 grams or more, we use the same process. We draw a vertical line from 130 on the 𝑥-axis to the curve and then draw a horizontal line from this point to the 𝑦-axis. We can read the cumulative frequency of 78 balls from the 𝑦-axis, which means that 78 balls had a weight less than 130 grams.

In order to find the number of balls that had a weight of 130 grams or more, we subtract this from the total frequency. The total frequency is the total number of balls that have been weighed. Hence, it is 100. Therefore, we have 100 minus 78, which is equal to 22. The answer to the second part of the question is that we estimate that there are 22 balls with a weight of 130 grams or more.

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