Chase asked the students in his class how many hours they studied during finals week. What is the range of values for the population?
Range: $\square$
Answer (2)
Identify the maximum value in the data set: 20.
Identify the minimum value in the data set: 1.
Calculate the range by subtracting the minimum from the maximum.
The range of the data set is 19 .
Explanation
Understanding the Problem We are given a table of data representing the hours students spent studying during finals week. Our goal is to find the range of this data, which is a measure of how spread out the data is. The range is calculated by subtracting the smallest value from the largest value in the dataset.
Finding the Maximum Value First, we need to identify the maximum value in the data set. Looking at the table, the values are: 4, 8, 6, 10, 5, 2, 9, 8, 9, 20, 10, 1, 15, 1, 8, 2. The maximum value is 20.
Finding the Minimum Value Next, we need to identify the minimum value in the data set. From the same list of values, the minimum value is 1.
Calculating the Range Now, we calculate the range by subtracting the minimum value from the maximum value: R an g e = M a x im u m − M inim u m = 20 − 1 = 19 Therefore, the range of the data set is 19.
Examples
Understanding the range of a dataset is useful in many real-life situations. For example, if you are tracking the daily temperature in your city, the range tells you the difference between the hottest and coldest days, giving you an idea of the temperature variability. Similarly, in finance, the range of stock prices can indicate the volatility of an investment. In education, understanding the range of test scores helps teachers assess the spread of student performance.
The range of values for the population of students studying hours is calculated by subtracting the minimum value from the maximum value. If the maximum study hours reported are 20 and the minimum is 1, then the range is 19. Thus, the range of study hours is 19 hours.
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