Ch. 1.4 Histograms & Stem-&-Leaf Plots

Transcription

1 Ch. 1.4 Histograms & Stem-&-Leaf Plots Learning Intentions: Create a histogram & stem-&-leaf plot of a data set. Given a list of data, use a calculator to graph a histogram. Interpret histograms & stem-&-leaf plots. Decide the appropriateness of a histogram & a stem-&-leaf plot for a given set of data. Histogram: a one-variable data display that uses bins (the width of each column) to show the distribution of values in a data set. Each bin corresponds to an interval of data values; the height of a bin indicates the number, or frequency, of values in that interval. Stem-&-Leaf Plot: a one-variable data display used to show the distribution of a fairly small set of data. Generally, the stem = left digit(s) of the data values & the leaves = the remaining value(s) to the right of the stem column. A key is usually included to give an example of how to read the chart.

2 CHOOSING THE NUMBER AND WIDTH OF YOUR BINS. Both of the histograms below show the same data. What makes them different? Does the histogram on the left represent more data than the one on the right? 1-2

3 Solution: Both of the histograms below show the same data. What makes them different? Does the histogram on the left represent more data than the one on the right? Answer: These histograms show the same data set but use different bin widths. Too many bins may create an info. overload; too few bins may hide some features of the data set. General rule: have 5 10 bins. 1-3

4 EXPLORING HISTOGRAMS AND THEIR RELATIONSHIP TO DOT PLOTS. The following dot plot shows in which year each penny in a stack was minted. Use the dot plot to create a histogram displaying the same data. 1-4

5 Solution: The following dot plot shows in which year each penny in a stack was minted. Use the dot plot to create a histogram displaying the same data. # of Mint Year 1-5

6 EXPLORING STEM-AND-LEAF PLOTS What part of the data display is the stem? What part of the display is the leaf? How are stem-and-leaf plots similar to histograms? 1-6

7 Solutions: What part of the data display is the stem? the column to the left of the red line What part of the display is the leaf? the numbers to the right of the red line How are stem-and-leaf plots similar to histograms? they both show shape & distribution (frequency) 1-7

8 YOU VISITED FOUR DIFFERENT STORES AND RECORDED THE PRICES ON 1-POUND BAGS OF POTATO CHIPS. USE THE STEM-AND-LEAF PLOT TO ANSWER THE FOLLOWING QUESTIONS. 1. What is the lowest price they found? 2. What do the entries in the third line from the top represent? 3. How many bags cost less than $2? 4. What is the most common price? 5. What is the range of prices for these chips? 1-8

9 SOLUTION: USE THE STEM-AND-LEAF PLOT TO ANSWER THE FOLLOWING QUESTIONS. 1. What is the lowest price they found? $ What do the entries in the third line from the top represent? $1.75 & $1.79 (the prices in the $1.70 s) 3. How many bags cost less than $2? 14 bags ($ s) 4. What is the most common price? $1.99 (there were 5 of these) 5. What is the range of prices for these chips? Range = Max Min = $2.59 $1.50 = $

10 #2.) P.63 Thirty students participated in a 20-problem mathematics competition. Here are the numbers of problems they got correct. {12, 7, 8, 3, 5, 7, 10, 13, 7, 10, 2, 1, 11, 12, 17, 4, 11, 7, 6, 18, 14, 17, 11, 9, 1, 12, 10, 12, 2, 15} 1. Construct two histograms for the data. Use different bin widths for each. 2. What patterns do you notice in the data? What do the histograms tell you about the number of problems that students tend to get correct? 3. Give the five-number summary for the data and construct a box plot. 4. Give the mode(s) for the data. 1-10

11 SOLUTIONS: #2.) P.63 Thirty students participated in a 20-problem mathematics competition. Here are the numbers of problems they got correct. {12, 7, 8, 3, 5, 7, 10, 13, 7, 10, 2, 1, 11, 12, 17, 4, 11, 7, 6, 18, 14, 17, 11, 9, 1, 12, 10, 12, 2, 15} 1. Construct two histograms for the data. Use different bin widths for each. Use bin widths of 2 for the number correct; then use a bin width of What patterns do you notice in the data? What do the histograms tell you about the number of problems that students tend to get correct? One observation is that student scores tended to be in the middle of the range. 3. Give the five-number summary for the data and construct a box plot. Min: 1 Q1: 6 Q2: 10 Q3: 12 Max: Give the mode(s) for the data. Mode: 7 & 12 # of students # correct 1-11