Finding the Mean of a Frequency Distribution ...

Question

Finding the Mean of a Frequency Distribution In Exercises 49–52, approximate the mean of the frequency distribution.

Populations The populations (in thousands) of the counties in Montana in 2019 (Source: U.S. Census Bureau)

Table displaying the population ranges in thousands and their corresponding frequencies for counties in Montana, 2019.

Accepted Answer

Hello everyone. Let's take a look at this question together. A group of volunteers recorded the number of hours they spent helping at a community center in a week. The data collected is grouped into the following frequency distribution, where we have our table of the hours spent and the frequency, approximate the mean number of hours spent volunteering in a week. Is it answer choice? A 11.1. Answer choice B 10.7, answer choice C 17.1, or answer choice D 11.7. So in order to solve this question, we have to use the frequency distribution data values to approximate the mean number of hours spent volunteering in a week. And we know that the first step in approximating the mean number of hours spent volunteering in a week. is to calculate the midpoints for each class using the formula for the midpoint, which is equal to the lower limit plus the upper limit divided by 2. So for the midpoint for the first class, which is 0 through 4 hours, we know we add 0 + 4 divided by 2, giving us the value of 2 for the midpoint for the first class. And then we can calculate the midpoint for the remaining classes. And then once we have the midpoint for all of the classes, we can multiply each midpoint by its frequency to get our F multiplied by X values, which in the following data table where we have our hours spent and our frequency, we have the remaining midpoint value. And multiplying the frequency and our midpoint, we get F multiplied by X, giving us the different values for F multiplied by X, and then we can take the sum of the F multiplied by X values to get 525. And using the data in the table, we can approximate the mean, The formula for the mean, which is equal to the sum of our F multiplied by x values divided by the sum of our F values, which looking at our table, we know that the sum of our F values is 45 and the sum of our F multiplied by X values is 525, so the mean is equal to 5. 125 divided by 45, which is approximately 11.7. Therefore, the approximate number of hours spent volunteering is 11.7. And looking at our answer choices, we can identify answer choice D as the correct answer, and all other answer choices are incorrect. I hope you found this video to be helpful. Thank you and goodbye.

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Finding the Mean of a Frequency Distribution In Exercises 49–52, approximate the mean of the frequency distribution.

Populations The populations (in thousands) of the counties in Montana in 2019 (Source: U.S. Census Bureau)

Key Concepts

Mean of a Frequency Distribution

Midpoint Calculation

Total Frequency

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Finding the Mean of a Frequency Distribution In Exercises 49–52, approximate the mean of the frequency distribution.Populations The populations (in thousands) of the counties in Montana in 2019 (Source: U.S. Census Bureau)