Presenting Quantitative Data With categorical data, the horizontal axis is the category, but with quantitative, or numerical, data we have numbers. If we have repeated values we can also make a frequency table. Example 9: A teacher records Quiz Frequency scores on a 20-point quiz for the Score of Students 30 students in their class. The 0 2 scores are: 5 1 12 1 19, 20, 18, 18, 17, 18, 19, 17, 20, 15 2 18, 20, 16, 20, 15, 17, 12, 18, 19, 18, 19, 17, 20, 18, 16, 15, 18, 20, 16 2 5, 0 and 0. 17 4 18 8 Here is a frequency table with 19 4 the scores grouped and put in order. 20 6 Using this table, it would be possible to create a standard bar chart from this summary, like we did for categorical data. However, since the scores are numerical values, this chart wouldn’t make sense; the first and second bars would be five values apart, while the later bars would only be one value apart. Instead, we will to treat the horizontal axis as a number line. This type of graph is called a histogram. between the bars. Here is a histogram for the data Histograms given above. Notice that in this histogram, the two A histogram is like a bar scores of 15 are to the right of 15, or between 15 and graph, but the horizontal axis 16. is a number line. Unlike a bar graph, there are no spaces for this reason. Some people choose to have bars The horizontal scales on at ½ values to avoid this ambiguity, as in this second histograms can be confusing histogram. If we have a large number of different data values, a frequency table listing every possible value would be way too long. There would be too many bars on the histogram to reveal any patterns. For this reason, it is common with quantitative data to group data into class intervals. Class Intervals Class intervals are groupings of the data. In general, we define class intervals so that: Each interval is equal in size. For example, if the first class contains values from the second class should include values from 135-149. We typically have somewhere between 5 and 20 classes, depending on the number of data values we’re working with.
Presenting Quantitative Data With categorical data, the horizontal axis is the category, but with quantitative, or numerical, data we have numbers. If we have repeated values we can also make a frequency table. Example 9: A teacher records scores on a 20-point quiz for the 30 students in their class. The scores are: 19, 20, 18, 18, 17, 18, 19, 17, 20, 18, 20, 16, 20, 15, 17, 12, 18, 19, 18, 19, 17, 20, 18, 16, 15, 18, 20, 5, 0 and 0. Here is a frequency table with the scores grouped and put in order. Quiz Score Frequency of Students 0 2 5 1 12 1 15 2 16 2 17 4 18 8 19 4 20 6 Using this table, it would be possible to create a standard bar chart from this summary, like we did for categorical data. However, since the scores are numerical values, this chart wouldn’t make sense; the first and second bars would be five values apart, while the later bars would only be one value apart. Instead, we will to treat the horizontal axis as a number line. This type of graph is called a histogram. Histograms A histogram is like a bar graph, but the horizontal axis is a number line. Unlike a bar graph, there are no spaces between the bars. Here is a histogram for the data given above. Notice that in this histogram, the two scores of 15 are to the right of 15, or between 15 and 16. The horizontal scales on histograms can be confusing for this reason. Some people choose to have bars at ½ values to avoid this ambiguity, as in this second histogram. If we have a large number of different data values, a frequency table listing every possible value would be way too long. There would be too many bars on the histogram to reveal any patterns. For this reason, it is common with quantitative data to group data into class intervals. Class Intervals Class intervals are groupings of the data. In general, we define class intervals so that: Each interval is equal in size. For example, if the first class contains values from the second class should include values from 135-149. We typically have somewhere between 5 and 20 classes, depending on the number of data values we’re working with.
Chapter3-Statistics9-7-18.docx