Grey Kangaroos are large, social marsupials, indigenous to Australia. The Eastern Greys are a light grayish brown, while the Western Grey is a copper brown color. As part of a study of the development of these creatures, biologists have measured various aspects of their skeletal structure. A sample of 124 palate widths was taken from skeletal remains and the data is presented in the stem-and-leaf plot below. The distributions of skeletal measures are generally thought to be approximately normal, which is consistent with the stem-and-leaf plot for this sample. The display uses five lines for each stem. Thus, "2t|" is the stem for palate widths of 22 and 23, "2f|" for 24 and 25, "2s|" for 26 and 27, and so on. (The "t" then stands for leaves that are twos and threes, the "f" for leaves of fours and fives, etc.) The mean palate width of this sample is 2.6 cm, and the standard deviation is 0.3 cm.
A graph shows palate width of grey kangaroos. The plot shows two sevens after one s, an eight then nine after one star, one zero then ten ones after two point, then eleven twos and thirteen fours after two t, then seventeen fours and ten fives after two f, then eleven sixes and seven sevens after two star, then six zeros and two ones after three period, then two twos and one three after three t.
Comment on the normality of the data based upon the stemplot.
The data in the stemplot appears to be approximately normally distributed. This is evident by the symmetrical shape of the plot, with the highest frequencies appearing around the center (where the mean is 2.6 cm) and tapering off towards the tails on either side. The presence of a few outliers does not significantly deviate from the overall shape, supporting the notion of approximate normality in the sample data.
Based on the stem-and-leaf plot provided, the data appears to be relatively normally distributed. The stemplot shows a symmetrical distribution with values centered around the mean of 2.6 cm. Additionally, the distribution appears to be relatively smooth, without significant gaps or outliers. These characteristics are consistent with the assumption of normality for the data.
Based on the stem-and-leaf plot provided, the distribution of palate widths for grey kangaroos appears to be relatively normal. The plot shows a symmetrical pattern, with the leaves extending evenly on both sides of the stems.
However, to make a more precise assessment of the normality of the data, it is often helpful to construct a histogram or a normal probability plot. These graphical methods can provide a visual representation of how closely the data adheres to a normal distribution.
To construct a histogram, you can group the palate width measurements into intervals (e.g., 20-22, 22-24, 24-26, etc.) and count the number of measurements falling within each interval. Then, plot the intervals on the x-axis and the corresponding frequencies on the y-axis. A bell-shaped histogram with a relatively symmetrical distribution would indicate normality.
Alternatively, a normal probability plot can be used to assess the normality of the data. This plot compares the observed data against a theoretical normal distribution. If the data points fall approximately along a straight line, it suggests that the data follows a normal distribution.
In summary, while the stem-and-leaf plot provides some evidence of normality, constructing a histogram or a normal probability plot will offer more conclusive insights into the distribution of the palate widths for grey kangaroos.