3. Describing Data Numerically
Describing Data Numerically Using a Graphing Calculator
1:22 minutesProblem 2.R.40
Textbook Question
In Exercises 37– 40, use the data set, which represents the model 2020 vehicles with the highest fuel economies (in miles per gallon) in the most popular classes. (Source: U.S. Environmental Protection Agency)
36 30 30 45 31 113 113 33 33 33 52 141 56 117 58
118 50 26 23 23 27 48 22 22 22 121 41 105 35 35
About how many vehicles fall on or below the third quartile?
Verified step by step guidance1
Step 1: Organize the data set in ascending order. This will help in identifying the quartiles accurately. Arrange the given values from smallest to largest.
Step 2: Determine the total number of data points in the set. Count the number of values provided in the data set.
Step 3: Calculate the position of the third quartile (Q3). Use the formula for the position of a quartile: Q3 = (3/4) * (n + 1), where 'n' is the total number of data points.
Step 4: Identify the value corresponding to the third quartile position. If the position is not an integer, interpolate between the two closest values in the ordered data set.
Step 5: Count the number of vehicles with fuel economy values less than or equal to the third quartile value. These are the vehicles that fall on or below the third quartile.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Quartiles
Quartiles are values that divide a data set into four equal parts, each containing 25% of the data. The third quartile (Q3) specifically represents the value below which 75% of the data points fall. Understanding quartiles is essential for analyzing the distribution of data, particularly in identifying outliers and understanding the spread of values.
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Data Set
A data set is a collection of related values or observations, often organized in a structured format. In this context, the data set consists of fuel economy values for various vehicles. Analyzing a data set involves calculating measures such as quartiles, means, and medians to summarize and interpret the information it contains.
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Descriptive Statistics
Descriptive statistics are statistical methods that summarize and describe the main features of a data set. This includes measures of central tendency (like mean and median) and measures of variability (like range and quartiles). These statistics provide a quick overview of the data, making it easier to understand trends and patterns, such as how many vehicles fall below a certain quartile.
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