Statistics, Day 2

Wednesday, Febuary 17th



We discussed the concepts of the 5-Number Summary, Interquartile Range (IQR) and the Box-and-Whisker Plot. Students have made Box & Whisker plots in previous math courses. To make this graph, students must first find the 5-Number Summay. The 5-Number Summary is made up of the following 5 numbers from the data set: minimum, lower quartile, median, upper quartile, and maximum. The interquartile range is used to show how the middle 50% of the data values are spread or are compacted. To find these values, the students need to follow these steps:

1. Order the data from least to greatest.
2. Identify the median.
3. Identify the median of the lower half of the data values. (Do not include the overall median in the lower half of the data values.) This is the lower quartile, also called the first quartile or simply Q₁.
4. Identify the median of the upper half of the data values. (Do not include the overall median in the upper half of the data values.) This is the upper quartile, also called the third quartile or simply Q₃.
5. Identify the smallest value (minimum) and the greatest value (maximum) of the data.
6. The interquartile range is found by subtracting the third quartile minus the first quartile.

To make a Box and Whisker Plot, follow these steps:

1. Create a number line or x-axis that spans at least from the minimum to the maximum values.
2. Use a short, vertical tic-mark to indicate the numbers in the 5-Number Summary in the space above the number line.
3. Draw a segment connecting the first two tic-marks for a "whisker" connecting the minimum to the first quartile.
4. Draw a segment connecting the last two tic-marks for a "whisker" connecting the third quartile to the maximum.
5. Connect the second and fourth tic-marks across the top and across the bottom to create a "box" around the middle 50% of the data values.

The numbers in the 5-Number Summary show how the data are spread or compacted. Each number occurs 25% of the way through the data values, however some of the distances between the actual data values are less (we talk about the these spans being more dense) or the distances between the actual data values are more (we talk about these spans being spread out).

Example:

Homework: Page 371, #1 - 9. Additionally, create a Box & Whisker Plot for #1 - 4 and #6 - 7.

Students received a project today. They need to select a measurable idea to compare between 2 populations (example, how many hours do boys vs. girls spend on Facebook?) and make a hypothesis about the expected results. They will have to collect at least 16 data values for each population (a minimum of 32 data values total). Then, they have to generate all of our statistics with each set of data: mean, mean absolute deviation (to be introduced tomorrow), and the 5-number summary. They need to make a Box & Whisker plot for both sets of data. They may make a histogram for extra credit. They then need to draw a conclusion based on the statistics. The final product can be a report, a poster, a PowerPoint, etc ... This project is due on Wednesday, February 24th.

There will be a test on Statistics (Unit 4 Part 2) on Friday, February 26th.

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