Section 7.6 Assessing Normality 335 Objective 4 Use stem-and-leaf plots to assess normality Stem-and-Leaf Plots Stem-and-leaf plots can be used in place of histograms when the number of stems is large enough to provide an idea of the shape of the sample. Like histograms, stem-and-leaf plots are excellent for detecting skewness. They are more useful for data sets that are not too small, so that some of the stems will contain more than one leaf. Stem-and-leaf plots are easier to construct by hand than histograms are, but histograms are sometimes easier to construct with technology. For example, the TI-84 Plus calculator will construct histograms, but cannot construct stem-and-leaf plots. Recall: Stem-and-leaf plots were introduced in Section 2.3. EXAMPLE 7.35 Use a stem-and-leaf plot to assess normality A psychologist measures the time it takes for each of 20 rats to run a maze. The times, in seconds, are 54 48 49 54 63 54 66 32 45 52 41 37 56 56 52 53 41 45 48 43 Construct a stem-and-leaf plot for these data. Is it reasonable to treat this as a random sample from an approximately normal population? 3 3 4 4 5 5 6 6 2 7 113 55889 223444 66 3 6 Figure 7.43 There are no outliers, strong skewness, or multimodality. Solution Figure 7.43 presents a stem-and-leaf plot of the times. The stem-and-leaf plot reveals no outliers, strong skewness, or multimodality. We may treat this as a sample from an approximately normal population. Check Your Understanding 1. For each of the following dotplots, determine whether it is reasonable to treat the sample as coming from an approximately normal population. a. 0 5 10 15 20 No b. 3 4 5 6 7 8 Yes 2. For each of the following histograms, determine whether it is reasonable to treat the sample as coming from an approximately normal population. (a) Yes (b) No a. 20 22 24 26 28 30 32 34 36 0.25 0.20 0.15 0.10 0.05 0 Relative Frequency b. 2 4 6 8 10 12 14 16 18 20 0.25 0.20 0.15 0.10 0.05 0 Relative Frequency 3. The following stem-and-leaf plot represents a sample from a population. Is it reasonable to assume that this population is approximately normal? No 1 34579 2 0278 3 25 4 37 5 38 6 4 7 8 1 9 6
navidi_monk_elementary_statistics_2e_ch7-9
To see the actual publication please follow the link above