Consider the following data. The summary statistics,...

Consider the following data. The summary statistics, histogram, and normal quantile plot were generated using Minitab. $$\begin{array}{lllllllllllllll}27 & 27 & 27 & 28 & 28 & 28 & 28 & 28 & 28 & 29 & 29 & 29 & 29 & 29 & 29 \\29 & 29 & 29 & 29 & 30 & 30 & 30 & 30 & 30 & 30 & 30 & 30 & 30 & 30 & 30 \\30 & 31 & 31 & 31 & 31 & 31 & 31 & 31 & 31 & 32 & 32 & 32 & 32 & 33 & 33 \\ 33 & 33 & 33 & 34 & 34 & & & & & & & & & &\end{array}$$ (a) Does the histogram indicate normality for the data distribution? Explain. (b) Does the normal quantile plot indicate normality for the data distribution? Explain. (c) Compute the interquartile range and check for outliers. (d) Compute Pearson's index. Does the index value indicate skewness? (e) Using parts (a), (b), (c), and (d), would you say the data are from a normal distribution?

Consider the following data. The summary statistics, histogram, and normal quantile plot were generated using Minitab.
$$\begin{array}{lllllllllllllll}27 & 27 & 27 & 28 & 28 & 28 & 28 & 28 & 28 & 29 & 29 & 29 & 29 & 29 & 29 \\29 & 29 & 29 & 29 & 30 & 30 & 30 & 30 & 30 & 30 & 30 & 30 & 30 & 30 & 30 \\30 & 31 & 31 & 31 & 31 & 31 & 31 & 31 & 31 & 32 & 32 & 32 & 32 & 33 & 33 \\
33 & 33 & 33 & 34 & 34 & & & & & & & & & &\end{array}$$
(a) Does the histogram indicate normality for the data distribution? Explain.
(b) Does the normal quantile plot indicate normality for the data distribution? Explain.
(c) Compute the interquartile range and check for outliers.
(d) Compute Pearson's index. Does the index value indicate skewness?
(e) Using parts (a), (b), (c), and (d), would you say the data are from a normal distribution?

Transcript

00:01 So we're looking at the data, and we can see that the data goes from 27 all the way up to 34.

00:07 And if we look at the histogram, the histogram looks to be, you know, pretty bell -shaped.

00:15 So we would think that this is approximately a normal distribution.

00:21 Then part b were to look at the normal quantile plot.

00:26 And remember, for a normal quantile plot, you're probably not ever asked to make one long, i never have had my students do that, but you are looking at those values and you're hoping that you're seeing some linearity and so approximately linear therefore the tendency is for the distribution to be approximately normal not perfect but not too bad then we want to look at on part c what the interquartile range is and we need to we have 50 numbers so if you have them all listed down, if you put them all on your calculator, your calculator will give it all to you with one one should put one variable stat but if you have 50 numbers and then you need to count to find the 25th number the 26 number and that number will be your median and that number ends up coming out to be 30 and then we have 25 numbers who are below and and so 25 numbers below, if i take 25 and divide it by 2, i get 12 .5.

01:41 So there are 12 numbers here, 12 numbers there.

01:44 We need the 13th number in the list counting this way.

01:49 And we also will need the 13th number counting this way.

01:53 This one will be our q1, and q1 comes out to be 29, and therefore q3 counting comes out to be 31.

02:05 And so our inner quartile range is the difference between q3 and q1 is two.

02:10 And so in order to find whether we have outliers or not, we want to take the q1 and we want to subtract away one and a half boxes.

02:24 So 29 minus 3.

02:27 Anything below 26 is going to end up being an outlier.

02:31 And there are none.

02:32 No low outliers.

02:33 And then we need to take q3 and add on one and a half boxes, box splits or iqrs.

02:42 So 31 plus 3 is 34.