Stem & leaf plots + histograms
- 1. By L.D.
- 2. Slide 3: Stem-and-Leaf Plots Slide 6: Mini Lesson: What If Slide 8: Mini Lesson Key 1 Slide 9: Mini Lesson: Key 2 Slide 10: Histogram Slide 12: Mini Lesson: The Difference Between Bar Graphs and Histograms Slide 13: Back to Back Stem-and-Leaf Plot Slide 17: Box-and-Whisker Plot Slide 20: Mini Lesson: Box Position Table of Contents
- 3. Example Problem: In the town of Sugar Pine, the next high temperatures for the next ten days are below. 63 F°, 63 F°, 65 F°, 66 F°, 73 F°, 75 F°, 78 F°, 81 F°, 81 F°, 82 F° Now we need to look at all the different numbers in the tenth place on the next slide. Stem-and-Leaf Plots
- 4. 63, 63, 65, 66, 73, 75, 78, 81, 81, 82 Now we need to look at all the different numbers that aren’t in the one’s place, there is 6, 7 & 8. We will place these on one side of the line and place the numbers that were tied to those numbers on the other side of the line on the next slide. Stem-and-Leaf Plots
- 5. 6 3 3 5 6 7 3 5 8 8 112 Stem-and-Leaf Plots Now that that is done, we need to give it the right format with a title, units and key. This will be on slide 7. Note: There are not any spaces between the numbers.
- 6. If one of the temperatures had been 9 F° and if one had been 134 F° and if one had been 3445 F°, it would have been looking like the below. Mini Lesson: What If 0 9 1 34 3 445
- 7. 6 3 3 5 6 7 3 5 8 8 112 High Temperatures For the Next Ten Days (Degrees Fahrenheit) Key: 6 I 3 = 63
- 8. A key can be ANY number in the problem. Mini Lesson Key 1
- 9. A key tells you what is between the lines, an example could be if you were working with decimals and you had the whole number on the left side and the other number on the other side. If your key number was 1.9 then the key would look like 1 I 9 = 1.9 Mini Lesson: Key 2
- 10. We will use the same set of numbers 63 F°, 63 F°, 65 F°, 66 F°, 73 F°, 75 F°, 78 F°, 81 F°, 81 F°, 82 F° We will arrange these on a graph, instead of categories we will have number ranges, for this one I will use a number range of 10, the amount of numbers that fit into that range will add up on the bar. Histogram
- 11. High Temperatures For the Next Ten Days 60 - 69 70 - 79 80 - 89 1 2 3 4 5 6 7 Frequency (Degrees Fahrenheit)
- 12. Mini Lesson: The Difference Between Bar Graphs and Histograms The key differences are that the bars touch in a histogram and they don’t in a bar graph. Another example is that the categories on a bar graph are words and on a Histogram they are numbers.
- 13. The back to back stem-and-leaf plot shows the prices (in dollars) of Poodles and Chihuahuas at a breeder. Compare the prices of adoption for the two dogs. This plot is on the next page. Back to Back Stem & Leaf Plot
- 14. Poodle 3 1 0 7 5 5 8 7 6 5 4 8 8 5 5 Adoption Prices 4 5 6 7 Chihuahua 0 0 2 3 3 1 1 2 3 5 5 0 2 2 2 Key: 4 I 6 I 0 = $64, $60
- 15. Poodle 3 1 0 7 5 5 8 7 6 5 4 8 8 5 5 Back to Back Stem & Leaf Plot 4 5 6 7 Chihuahua 0 0 2 3 3 1 1 2 3 5 5 0 2 2 2 Key: 4 I 6 I 0 = $64, $60 So this is how it works, cover up the Poodle side with your hand. Look at the other stem- and-leaf plot on slide 5, don’t they look similar? You read the Chihuahua side like the other plot was read. To read the Poodle plot, cover up the Chihuahua side and imagine the “middle column” on the left side. The key is read much the same way, when you cover up the 4 and look on the other side of the equal, you see $60. When you cover up the 0 and switch the 4 and 6 with your eyes, you see 64 or $64.
- 16. Poodle 3 1 0 7 5 5 8 7 6 5 4 8 8 5 5 Back to Back Stem & Leaf Plot 4 5 6 7 Chihuahua 0 0 2 3 3 1 1 2 3 5 5 0 2 2 2 Key: 4 I 6 I 0 = $64, $60 Now we need to find the median of the prices of Poodles and the median of prices for Chihuahuas. To do this we will cross out the right and left sides of each one separately to find the middle or median. Poodle Median: 67 Chihuahua Median: 53 Conclusion: In general, Poodles cost more than Chihuahuas from breeders.
- 17. Find the median, lower quartile and higher quartile. Also find the maximum and minimum. Box-and-Whisker Plot
- 18. 20 22 27 31 46 47 54 Median: 31, the number that splits it in half. Lower Quartile: 22, the half of the smaller numbers Higher Quartile: 47, the half of the larger numbers Minimum: 20, smallest number. Maximum: 54, biggest number. Now you need to place these things on a numbered line (next slide). Box-and-Whisker Plot
- 19. 10 20 30 40 50 60 70 80 90 Box-and-Whisker Plot minimum maximum median Higher Quartile Lower Quartile
- 20. It doesn’t matter that the box was floating since there is no scale, but if there was a scale, the box would be would be flat on the line. Mini Lesson: Box Position
- 21.