17.6 Median, Lower and Upper Quartiles Common Core Standards 7.SP.1. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. 7.SP.2. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be. 7.SP.3. 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. 7.SP.4. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.
WARM-UP (1) 1) Put the number in order from least to greatest. 15, 4, 19, 7, 56, 12, 7
2) When you put them in order, what number is in the middle?
2) Find the minimum, maximum, and range.
Median, Lower and Upper Quartiles What three numbers can help us divide data into four equal sized groups?
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20
5.5
10.5
15.5
NOTES (2) The median is the middle number when the data is in order from least to greatest. Examples Find the median of the seven numbers. 17, 5, 22, 9, 13, 22, 29
NOTES (3) The Lower Quartile is the middle number of the lower half of the data. The Upper Quartile is the middle number of the upper half of the data. Examples Find the minimum, maximum, median, lower quartile, and upper quartile of the data. 145, 264, 76, 12, 75, 32, 265
NOTES (4) Sometimes you need to create a middle number to find the median, lower, and/or upper quartile. Note: The median is in neither half of the data. Examples Find the median, lower quartile, and upper quartile of the numbers. 14, 5, 18, 24, 10, 3
11, 20, 24, 30, 23, 18, 7, 14, 2
NOTES (5) A box plot displays the minimum, maximum, median, lower and upper quartiles graphically. Example Find the minimum, maximum, median, lower and upper quartiles from the box-and-whisker plot.
19
24
45 34.5
50
EXAMPLES (6) Find the minimum, maximum, median, lower and upper quartiles from the box plot.
10
20
30
40
50
EXAMPLES (7) Find the minimum, maximum, median, lower and upper quartiles from the box plot.
2 4 6 median _____
8
minimum _____ maximum _____ lower quartile _____ upper quartile _____
10 12 14 16 18 20 22
PRACTICE (8) The amount of hours worked per week for 7 employees is shown below. Find the minimum, maximum, median, lower quartile, and upper quartile of the data. 55, 34, 45, 46, 17, 28, 40
PRACTICE (9) Below is the plot of the number of defects found in new cars being manufactured at a local auto plant.
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2
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6
7
8
9
10
11
What was the median number of defects found? _____ What was the maximum number of defects found? _____ What was the Upper Quartile? _____
FINAL QUESTION (10) Below is the plot of the number of defects found in new cars being manufactured at a local auto plant.
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2
3
4
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7
8
What was the minimum? _______ What was the Lower Quartile? _____
9
10
11
