Distribution refers to the arrangement of data around the mean. Randomly sampled data from a normal population should be normally distributed (Camm et al., 2018). Normal distribution occurs when the probabilities of data assume a bell-shaped curve. The curve describes the arrangement of data around the mean such that data is concentrated around the mean and decreases with the distance from the mean (Weisstein, 2002). The mean is at the center of the bell shape, while the mean's distance represents the standard deviation. A normal distribution is symmetrical around the mean.
Table 1 : Descriptive Statistics
| Mean |
185.8687 |
| Median |
185.0000 |
| Standard Deviation |
9.9314 |
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A random sample from a normally distributed population is approximately normally distributed. According to the central limit theorem, the sample approaches a normal distribution as the sample enlarges (Camm et al., 2018). The descriptive statistics of a sample may be used to assess the nature of the distribution. A sample is said to have normal distribution if the mean is equal to the median (Camm et al., 2018). Otherwise, a mean greater than the median implies that the data is positively skewed, while a mean less than the median implies that the data is negatively skewed (Camm et al., 2018). The mean is slightly greater than the median implying height data is slightly positively skewed.
Figure 1 : A histogram for Height (cm)
Figure 2 : Stem and Leaf Diagram for Height (cm)
| stem | leaf |
| 16 | 028 |
| 17 | 00235555577888888889 |
| 18 | 0000000000003333334555555555567888888888888889 |
| 19 | 0111111113333366668888 |
| 20 | 113688 |
| 21 | 111 |
The distribution of data can be represented graphically using a histogram or stem and leaf diagram. The graphs represent the arrangement of data around the center. Both the histogram and stem and leaf show that slightly more data is concentrated on the right (Camm et al., 2018). This means that the data is slightly positively skewed to the right. However, the data is mostly arranged in a bell-shaped curve, meaning that height data is approximately normally distributed (Figure 1-2).
Figure 3 : Normal Distribution Curve
A set of data's normal distribution curve is plotted as a graph of normal probabilities against the data values. The probability density function of normal probabilities is f (x) =
*
(Weisstein, 2002). A plot of normal probabilities against the data values produced a bell-shaped curve that is symmetric around the mean (Figure 3).
. In conclusion, an analysis of the height data shows that the data assumes an approximately bell-shaped curve. The data is, therefore, approximately normally distributed, meaning that normal distributions actually exist.
References
Camm, J. D., Cochran, J. J., Fry, M. J., Ohlmann, J. W., and Anderson, D. R. (2018). Essentials of business analytics. Cengage Learning.
Weisstein, E. W. (2002). Normal distribution. https://mathworld. Wolfram. Com/.
