Question

#1 - What is the general distributional shape (in terms of normality, skewness, kurtosis) of the histograms represented in histogram below?

12 12 10 10 Std. Dev 1.23 Z 2 Mean -0.5 N 20.00 Std. Dev1.36 Mean-1.0 N 20.00 -4.0-3.0-2.0-1.0 0.0 1.0 3.0-2.0-1.0 0.0 1.0 Before software use Before software use visualization with screen visualization with glasses Figure 6: Orbitals-histograms showing the differences between: a) results before software use and results with screen visualization; b) and results before software use and results with visualization through stereoscopic glasses

2.) The legend below indicates that the whiskers represent the standard deviation, the box represents the standard error, and the line represents the median. Have I represented the elements of the boxplot correctly? If not, what is incorrect?

The grade point averages of our Physics and Chemistry students lie between values of 11 and 16 (out of 20), with an average of 13.5, a median of 13.0 and standard deviation of 1.5. Concerning software, our sample students have a good knowledge of common computer applications (spreadsheets, word processor, browsers, etc) as well as with pedagogical software, eg, Interactive Physics, from Knowledge Revolution, and Creative Physics, from Stewart Software. None of the students had used virtual reality before the study. Regarding their spatial aptitude, spatial comprehension is more homogeneous than spatial reasoning, with 3⁄4 of the data over 19 (first quartile), and an upper median (20). Spatial reasoning is less homogeneous, with 3⁄4 of the data lower than 20, and a median of 16 (Figure 3).

Answer 1

1. Since in both cases the longer tail of the distributions are towards the lower values of the variables so both distributions are negatively (left) skewed.

2.

First quartile<median<3rd quartile so it should be:

Not correct.

length of Box=Third quartile-first quartile=inter quartile range (IQR)

So it should be median-first quartile(instead of median-standard error)

AND

3rd quartile-median (instead of median+standard error).

"the whiskers represent the standard deviation" is wrong. This should be

Upper whisker=3rd quartile+1.5*IQR

Lower whisker=3rd quartile-1.5*IQR

Indication of median is correct.