Probability Statistics Displays of Quantitative Data Quantitative Data

Probability & Statistics Displays of Quantitative Data

Quantitative Data Dealing With a Lot of Numbers… n n Summarizing the data will help us when we look at large sets of quantitative data. Without summaries of the data, it’s hard to grasp what the data tell us. The best thing to do is to make a picture… We can’t use bar charts or pie charts for quantitative data, since those displays are for categorical variables.

Quantitative Data Displays of Quantitative Data ·Histogram ·Stem-and-Leaf ·Dot plot

Quantitative Data Displays of Quantitative Data · Box Plots are also used to display quantitative data, but we will not discuss box plots until the next unit.

Quantitative Data Histogram: · A graph used to display quantitative data. · imilar to a bar graph (with no spaces). · umbers are grouped into equal width piles alled BINS. There are 9 bins in this graph. (one of the bins is empty) If thedatavalues were between only The made up would of whole 5 and 10 be numbers, numbers stacked inonly this bin. 5, 6, 7, 8, and 9 would (including 5 but not be stacked this bin. includingin 10) 5 ≤ P < 10 The bin size here is 5. (Each stack is 5 units wide. ) If a value falls on the border of two bins, we usually put the value in the bin to the right.

Quantitative Data This histogram could represent the following data: -18, -16, -12, -11, -7, -6, -5, -4, -4, -3, -3, -3, -2, -2, -1, -1, 1, -1, 0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 6, 6, 7, 7, 9, 12, 22 That is because the data only has 5 numbers between the numbers 5 and 10. Notice that the bin containing numbers between 5 and 10 is also 5 units high. This bin is empty. The data does not contain any numbers between 15 and 20.

Quantitative Data This histogram could represent the following data: -18, -16, -12, -11, -7, -6, -5, -4, -4, -3, -3, -3, -2, -2, -1, -1, 1, -1, 0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 6, 6, 7, 7, 9, 12, 22 Can you tell how tall this bin is? Answer: 21 units high Count the number of data values that are between 0 and 5. Remember, that 0 is included in this bin.

Quantitative Data This histogram could represent the following data: -18, -16, -12, -11, -7, -6, -5, -4, -4, -3, -3, -3, -2, -2, -1, -1, 1, -1, 0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 6, 6, 7, 7, 9, 12, 22 Find the height of each of the other bins. The bins are labeled as a range of data. For example, this bin is labeled as 0≤P<5

Quantitative Data Stem-and-Leaf Displays Usually done by hand therefore used for a relatively small amount of data (approx. 10 to 100 numbers) Leaf Stem -45, -32, -17, -16, -14, -12, -9, -7, -7, -5, -4, -3, -2, 1, 3, 5, 6, 7, 8, 8, 8, 12, 15, 21, 22, 24, 33, 41, 43, 56 If you tilt your head to the right your eyes a little, you can Thisand rowblur represents the numbers a stem-and-leaf plot looks 21, see 22, that and 24. like a histogram.

Quantitative Data Stem-and-Leaf Displays You can also make a double stem-and-leaf plot. (This format is convenient for comparing two related sets of data) Stem Write the data that is represented by the female side of this stemand-leaf plot. How many males are represented in this plot?

Quantitative Data Dot plots Similar to a stem-and-leaf plot, but instead of the digits, a dot is placed next to each stem. A double dot plot Dot plots are usually generated by computers and graph a large amount of data.

Quantitative Data Dot plots n n The dot plot to the right shows Kentucky Derby winning times, plotting each race as its own dot. You might see a dot plot displayed horizontally or vertically.

Display Quantitative Creating Displays of Quantitative Data • Histograms • Stem & Leaf Plots • Dot Plots

Display Quantitative Steps to creating a Histogram. 1. Put the data in order (from least to greatest) 2. Determine the range of data that needs to be displayed 3. Determine an appropriate bin size 4. Determine how high the largest stack (bin) will be and adjust the frequency scale so that it will fit on the graph. 5. Draw the bars for the Histogram 6. Put a title on the graph and the axes.

Display Quantitative Example: The following data lists the test grades of 60 girls and boys in a math class.

Display Quantitative The first step in creating a display of quantitative data is to put the data in order. Go back if you haven’t finished yet. Take your time! Be careful! Use the space provided in your notes to put the data Your data should look like this. in order from least to greatest.

Display Quantitative Next, determine the range of data that needs to be displayed. With a minimum value of 25 and a maximum value of 99, the range of the data is 99 – 25 = 74

Display Quantitative Next, determine and appropriate bin size. A good rule of thumb is to create a graph that contains at least 7 or 8 bins. Note: The x-axis does not need to show x = 0. The first bin just needs to show the minimum data value. With a range of 74, if we used a bin size of 8, there would be 10 bins. 1 2 3 4 5 6 7 8 9 10

Display Quantitative If we used a bin size of 10, there would be 8 bins. 1 2 3 4 5 6 7 8 Because the data is made up of test scores, the appropriate bin size is probably 10. This way, we can clearly see how many students received A’s, B’s, C’s, etc.

Display Quantitative Next, we need to determine the largest stack so that we can set the scale on the frequency axis. Because our biggest stackare (bin) will be 90 17 and units high, the There are 14 values that less than greater 10 100 and There are 17 values that are less than 80 and greater frequency axis has to range from zero to at least 17. than or equal to 80. 80 ≤ s < 90 greater than or equal to 90. 90 ≤ s < 100 than or equal to 70. 70 ≤ s < 80 (Remember, that zero must be included in the frequency axis. ) This is our largest stack!

Display Quantitative The following graph has 10 tick marks (boxes) available for each axis. To fit 17 units on the vertical (frequency) axis…. 20 18 16 14 12 10 Scale = 2 8 6 4 Using a scale of 10 on the horizontal scale will allow us all 8 bins that we need. 2 10 20 30 40 50 60 70 80 90 100

Display Quantitative Next, let’s draw the graph. Math Test Grades 20 One 30 number in the The ≤ s < 40 bin One number in Seven numbers in the Ten numbers in the 20 ≤ s < 30 bin is empty. 40 ≤≤ ss << 50 bin Seventeen numbers in 50 60 bin Fourteen numbers in 60 ≤numbers s < 70 bin Ten in bin the 70 ≤ s < 80 the≤ 80 s < 90 90 s <≤ 100 binbin Don’t forget the labels! Number of Students 18 16 14 12 10 8 6 4 2 10 20 30 40 50 60 70 80 90 100 Scores

Display Quantitative Stem & Leaf Plots and Dot Plots are drawn almost exactly as Histograms are drawn. If you blur your eyes just a bit while looking at Stem & Leaf plots and dot plots, you can see that they are really the same type of display.

Display Quantitative Oncefollowing we organize theages dataof into The are the female ascendingof order, we can easily draw a members an orchestra. stem & leaf plot. 41, 15, 55, 18, 60, 21, 72, 26, 21, 29, 15, 29, 18, 41, 29, 42, 46, 61, 48, 29, 55, 26, 60, 46, 61, 48 72 A double stem & leaf plot would be a nice way to compare male and female members of the orchestra. Ages of male members: 10, 12, 15, 21, 33, 35, 35, 42, 45, 51, 56, 58, 59, 60, 65, 66, 70, 71, 72 For this data, the 10’s digit would be the proper stem.

Display Quantitative The stem & leaf plot drawn in the previous example, could also be drawn as a dot plot. For the dot plot, The “stem” would display the scale in the same way as a histogram. The “leafs” would be displayed by dots instead of by specific numbers. Female members: 15, 18, 21, 26, 29, 41, 42, 46, 48, 55, 60, 61, 72 Male members: 10, 12, 15, 21, 33, 35, 35, 42, 45, 51, 56, 58, 59, 60, 65, 66, 70, 71, 72 10 20 30 40 50 60 70

Try this. Display the following data using a histogram with bin size 5. (use the grid provided in your notes)