Notes 2.3: Graph Quantitative Data



Learning Target Graph Quantitative DataLet’s quickly review…Quantitative Data: Quantitative data can be graphed using a dot plot, stem plot, and histogram. (Box plots are used too, but we’ll learn those later this unit!)? I can graph and interpret a dot plot ?Dot Plots: A set of quantitative data represented by using dots over a number line. Useful with smaller data sets.480758510804100Example 1: Use the dot plot showing results from a survey asking “How many hours do you exercise each week?” to determine how many people responded to the survey.Example 2: Create a dot plot for the following ages of students: 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 17, 18, 18Step 1: Draw and label the horizontal axis (number line) that includes all of your data.Step 2: Place one dot for each data point (Be sure to use same size dots and stack repeats)Step 3: Title your graph244983015430500? I can graph and interpret a stem plot ?Stem Plots: A plot where data is separated into a stem and a leaf. The stem (vertical) may contain more than one digit, but the leaf (horizontal off of the stem) only contains the smallest digit. Every value in the leaf represents a number. Useful with smaller data sets. Ages of customers4546600825500Example 3: What does the key represent in this stem plot? Be specific and include the context of the graph in your explanation.Example 4: Create a stem plot for the following test scores: 73, 42,?67, 78, 99, 84, 91, 82, 86, 94Step 1: Order your data from smallest to largestStep 2: Determine the digit for the leaf (smallest) and the values for the stemStep 3: Write your stem values vertically in the stem column (do not skip numbers)Step 4: Add the single digit for each leaf horizontally across from its corresponding stem. Any value in the leaf represents a value in the data set. Do NOT separate values in leaves with commas!!Step 5: Include title and keyOrder data from smallest to largest: 42, 67, 73, 78,?82,?84, 86,?91,?94,?99Example 5: If you have too many leaves in one row, you can make a split stem plot. The goal of a stem plot is to try and get a nice curve.Number of touchdown passes in a season:37, 33, 33, 32, 29, 28, 28, 23, 22, 22, 22, 21, 21, 21, 20, 20, 19, 19, 18, 18, 18, 18, 16, 15, 14, 14, 14, 12, 12, 9, 6The stem plot is on the left. Notice there are a lot of values in each row.To split the stem: Use digits 0 – 4 for the first stem and 5 – 9 for the second. A split stem plot of the data is shown on the right. Notice how the split stem shows a better curve.Touchdown passesTouchdown passes0 | 6 90 | 1| 2 2 4 4 4 5 6 8 8 8 8 9 9 0 | 6 92 | 0 0 1 1 1 2 2 2 3 8 8 91 | 2 2 4 4 43 | 2 3 3 7 1 | 5 6 8 8 8 8 9 9 2 | 0 0 1 1 1 2 2 2 3Key: 3 | 2 = 322 | 8 8 93 | 2 3 3 3 | 7If you are comparing two data sets, you can create a back to back stem plot. One set of data will have leaves to the right of the stem (as usual). The other set of data will have leaves to the left of the stem (with the smallest values closest to the stem). 41624259271000Example 6: Which brand has the better phone battery?Justify your conclusion using the back to back stem plot.Example 7: Create a back to back stem plot to compare the price of a concert at local venues and the price of the same concert at international venues. They have been put in order for your convenience Local ticket prices (in US $): 20, 25, 25, 25, 28, 30, 30, 34, 35, 35, 38, 40, 40, 40, 45, 45, 46, 49, 50International ticket prices (in US $): 30, 40, 50, 55, 56, 58, 59, 61, 63, 75, 78, 80, 80, 81, 84, 95, 96, 99, 100? I can graph and interpret a histogram ?Histograms: Data is represented with rectangular bars. Histograms represent quantitative data and the bars touch each other. The horizontal axis includes the values and the vertical axis contains the frequency (how often each value occurs). Histograms are useful with larger data sets.484822510604500Example 8: How does a histogram differ from a bar graph?Example 9: Justify why a histogram is appropriate to represent the heights of Black Cherry Trees and a bar graph would NOT be an appropriate choice to display the data.Example 10: Create a histogram to display the following heights of students heights (in inches): 68, 67, 64, 68, 64, 51, 60, 57, 61, 65, 60, 62, 64, 68, 58, 54, 52, 50, 48, 50, 55, 58, 60, 65, 68, 57, 68, 70, 52, 56, 55, 71, 67, 49Step 1:?Draw and label your x and y axis. Step 2:?Choose the number of bins or classes for the x axis (usually between 5 and 10). Decide on the increments for the scale and label your graph. Step 3: Create a frequency table to count the number of values in each bin. Use tally marks. If you are at the end of a class (bin), round up to the next bin.35807653048000ClassFrequency45 – 50| |50 – 5555 – 6060 – 6565 – 7070 – 75Step 4:?Create a rectangular bar in each bin that corresponds to the appropriate frequency for each class.Step 5: Title graph? I can describe the distribution of quantitative graphs using SOCS ?399542023177500Distribution: Describes the pattern of a quantitative data set (SOCS)S: Shape. Describe the overall data patternSymmetrical: Balanced/same on both sides. Mirror image (can be approximately symmetrical).Skewed Right: Most of the data is towards the left of the graph. There is a tail (skew) to the right.Skewed Left: Most of the data is towards the right of the graph. There is a tail (skew) to the left.43719756921500O: Outlier. Describe data that is far away from the rest of the data setC: Center. Describe the location of the middle of the data setS: Spread. Describe the overall spread of the dataExample 11: Describe the distribution (SOCS) of the following histograms.2657475111125005124450825500313690508000 b.c.Example 12: Describe the distribution (SOCS) of the stem plot.54292515875000Key: 6 | 9 = 69? I can identify misleading quantitative graphs ?Example 13: What is misleading about this dot plot?15335254953000203835015811500Example 14: What is misleading about this histogram? ................
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