Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.
In order from least to greatest, here are the prices per gallon of gas at two different gas stations over the past 7 days.
Station A:
2.38, 2.68, 2.82, 2.86, 2.99, 3.26, 3.59
Station B:
2.84, 2.85, 2.88, 2.95, 2.98, 3.03, 3.05
Suppose that these gas stations were the closest to your house, but not near each other. Which gas station would you go to for gas? Explain your reasoning.
11.3
Activity
Which One’s Best? (Part 2)
Standards Alignment
Building On
Addressing
6.SP.5
Summarize numerical data sets in relation to their context, such as by:
Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.
For each pair of data, decide which one you would choose. Use the median and interquartile range to support your choice.
A family is trying to decide which restaurant to go to. Here are each restaurant’s health inspection ratings over the past year. Considering the restaurants’ ratings, which restaurant should the family go to?
At the end of last year, teachers were rated by their students on a 0–10 scale. Two of the teachers’ ratings are given. Whose class would you register for? Explain your reasoning.
Teacher A: 9, 8, 10, 10, 7, 1, 8, 1, 2, 8
Teacher B: 9, 8, 8, 7, 9, 7, 7, 9, 7, 8
Glossary
None
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Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.
Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.