Chapter 2. Frequency distribution. Summarizing and Graphing Data

Transcription

1 Frequency distribution Chapter 2 Summarizing and Graphing Data Shows how data are partitioned among several categories (or classes) by listing the categories along with the number (frequency) of data values in each item 1 2 Example: IQ Scores and Lead Exposure Frequency Distribution: IQ of Low Lead Group Original data: Lower Class Limits the smallest numbers that can belong to different classes. (Table 2.2 has lower class limits of 50, 70, 90, 110, an 130.) Upper Class Limits the largest numbers that belong to different classes. (Table 2.2 has upper class limits of 69, 89, 109, 129, and 149.) Class Midpoints the values in the middle of the class. Each class midpoint is found by: Table 2.2 has class midpoints 59.5, 79.5, 99.5, 119.5, Class Boundaries numbers used to separate classes, but without the gaps created by class limits Figure 2-1 shows the gaps created by class limits in 2-2. The class boundaries are in the center of those gaps Class Width the difference between two consecutive lower class limits in a frequency distribution. Table 2-2 uses class width of 20. &

2 Procedure for Constructing a Frequency Distribution 1. Select the number of classes (usually between 1 and 20) 2. Calculate the class width Use the data below to construct a frequency table for pulse rates of females. Use seven classes. 3. Choose the value for the first lower class limit (minimum data value or convenient value below the minimum) 4. Using the first lower class limit and class width, list the other lower class limits 5. Determine upper class limits 6. Take each individual data point and put a tally in the appropriate class. Add tallies to find frequency of each class It was given to use 7 classes 1. Frequency Table for Female Pulse Rates 2. The minimum data value is 60, so we ll use it for the first lower class limit. 3. Using 1, 2, and 3 we have lower class limits: = = = = = = use classes 60-69, 70-79, 80-89, 90-99, Pulse Rates of Females , Pg. 52 #19 Heights of statistics students were obtained by the author by part of an experiment conducted for class. The last digit of those heights are listed below. Construct a frequency distribution with 10 classes. Based on the distribution do the heights appear to be reported or actually measured? What do you know about the accuracy of the results? Answer These heights appear to be reported since the frequencies of 0 and 5 are significantly higher, which tends to result from people approximating their height. Hence, these results probably aren t very accurate

3 Relative Frequency Distribution each class frequency is replaced by a relative frequency (or proportion) Percentage Frequency Distribution each class frequency is replaced by a percentage Note: In our book they use the term relative frequency distribution whether they use relative frequencies or percentages Example of normally distributed data 17 18

4 A Normal distribution is characterized by two numbers: 1. Center (most typical data value) 2. Width (degree of variation of data values); also called spread or variability of data values Histogram graph consisting of bars of equal width drawn adjacent to each other. The horizontal scale represents classes of quantitative data and the vertical scale represents frequencies. The heights of the bars correspond to the frequency values

5 25 26 Normal Quantile Plot The population distribution is normal if the pattern of points in the normal quantile plot is reasonably close to a straight-line and the points do not show some kind of systematic pattern that is not a straight line pattern 55 Not Normal: The points do not lie reasonably close to a straight line The points show some systematic pattern that is not a straight-line pattern

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