Question

Is the sample average number of children a good measure of the typical number of children, and why or why not and does it appear that the sample distribution is approximately normal?

Investigate the distribution of women's number of children (children). Report the average, standard deviation, minimum, maximum, median and the 10th 25th, 75th and 90th percentile of its sample distribution. Also produce a histogram for children. Given your findings, is the sample average number of children a good measure of the typical number of children, and why or why not? Does it appear that the sample distribution is approximately normal? 2.25975 Mean 2.218673 Std Dev Minimum 12 Maximum Median Percentiles 10th 25th 4 75th 6 90th 15 10 number afliving children

Answer 1

Here, the sample average number of children is not a good measure of the typical number of children, i.e., the number of children in the population, because the data is skewed in nature, so by the properties of sample average or sample mean, it loses its ability to provide the best central location of the data. In this case, the sample median, which is not influenced by the skewed values and retains its position is the best measure for the typical number of children in the dataset.

In a normal distribution, the density curve is symmetrical, bell-shaped in nature with mean at the peak of the curve in the center. In the given density graph, it shows a highly positively skewed structure, far from symmetry. Hence it doesn't appear that the sample distribution is approximately normal in nature.