Constructing a Frequency Distribution and a Relative Frequency...

Question

Constructing a Frequency Distribution and a Relative Frequency Histogram In Exercises 37–40, construct a frequency distribution and a relative frequency histogram for the data set using five classes. Which class has the greatest relative frequency and which has the least relative frequency?

Taste Test

Data set: Ratings from 1 (lowest) to 10 (highest) provided by 36 people after taste-testing a new flavor of protein bar 2 6 9 2 9 9 6 10 5 8 7 6 5 10 1 4 9 3 4 5 3 6 5 2 4 9 2 9 3 3 6 5 1 9 4 2

Accepted Answer

Hello, everyone. Let's take a look at this question together. A teacher recorded the test scores from 1 to 10 of 35 students in a mathematics class, giving us the following values for the test scores from 1 to 10. Using 5 classes, construct a relative frequency histogram where we express relative frequencies as percentages. Which class interval contains the largest proportion of scores and which contains the smallest. So in order to solve this question, we have to recall how to construct a relative frequency histogram using 5 classes, and then determine which class interval contains the largest proportion of scores and which contains the smallest. And so the first step to solving this problem is to find the range of the data, which looking at our data set, we know that the lowest score is 1, and the highest score is 10, and the range is calculated as the highest score, which is 10, subtracted by the lowest score, which is 1, giving us 9. And using the value for the range, we can then determine the class width. Where we divide the range by the number of classes. So, the class width is equal to 9 divided by 5, giving us an approximate class width of 2. And now that we have the class width, we can define the class intervals. Where we start at 1 and use a width of 2, giving us the following class intervals for our 5 classes. And then we tally the frequencies for each class, which involves counting how many scores fall into each interval. And for the first class interval, which is 1 through 2, we know we have 4 scores. For the 2nd class interval of 3 to 4, we have 6 scores. For the 3rd class interval, which is 5 through 6, we have 10 scores. For the 4th class interval, which is 7 through 8, we have 9 scores. And lastly, for our 5th interval of 9 through 10, we have 6 scores. And then we can calculate the relative frequencies, which we are calculating them as a percentage. And for the first class interval, we have 4 divided by 35, which is the total score, multiplied by 100%, giving us approximately 11.4% for the first class interval. And then we calculate the relative frequency in percentage or the remaining 4 class intervals, giving us their relative frequencies, and then using the values for the relative frequencies of each of the 5 classes, we can construct the relative frequency histogram. Where we know the height of each bar shows the relative frequency, which is how often values occur relative to the total number of values, and it is expressed as a percentage in this case. And so we end up with the following relative frequency histogram of the test scores with our 5 class intervals on the X axis, and their relative frequency as a percentage on the Y axis. And looking at our histogram, we know we need to identify the largest and smallest proportions. which we can see that the largest proportion is in the 5 to 6 class interval, which is 28.6%, and the smallest is in the 1 to 2 class interval, which is 11.4%. Therefore, we have the following relative frequency histogram, and we know which intervals contain the largest proportion and the smallest proportion. And looking at our answer choices, we can identify that answer choice A is 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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Key Concepts

Frequency Distribution

Relative Frequency

Histogram

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