Question

5.5.18 Generate a sample of 30 from an N(10, 2) distribution and a sample of 1 from an N (30, 2) distribution. Combine these together to make a single sample of 31. (a) Produce a boxplot of these data b) What do you notice about this plot? (c) Based on the boxplot, what characteristic do you think would be appropriate to measure the location and snread of the distribution? Exnlain whv

Answer 1

From the boxplot we find the following things

1. First Quartile, Q1 = 8.97653

2. Median = 10.5594

3. Third Quartile = 2.29049

4. Whiskers to: 6.38556, 13.2207

5. One outlier is present. The value is 31.9955

6. The distribution is positively skewed

Since the data contain an outlier, we can not use moment measures of location and spread. Because, those measures depend upon all the observations. Hence, the effect of only a single observation can be severe to these measures. So, we depend on quantile measures of location and spread. Because, these do not depend upon all the observations, more precisely, on extreme observations and hence are more robust in nature. Here we will use median as a measure of location and quartile deviation as a measure of spread. Median = 10.5594 and Quartile deviation = 1.145245.