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(c) Descriptive statics, histogram and box-and-whisker plot for “Gross”
Descriptive statics for entire population
Variable N N Mean SE Mean StDev Minimum Q1 Median Q* Gross 331 0 31671589 2159782 39293782 1065431 7487370 18552460 37771017 Variable Maximum Gross 306137970
Descriptive statics for random sample
Variable N N Mean SE Mean StDev Minimum Q1 Median Q* Gross 30 0 25748158 4346332 23805840 2410162 8448098 19158752 33442303 Variable Maximum Gross 105410874
Box-and-whisker plot for entire population
Box-and-whisker plot for random sample
Histogram for entire population *The graph is based on a range of 0 to 320000000 and a class width of 10000000
Histogram for random sample *The graph is based on a range of 0 to 120000000 and a class width of 10000000
The four basic features and comments:
- Central tendency for entire population is at 0-10000000. Central tendency for the random sample is also at 0-10000000, although the number of cases appeared in this bin is only slightly higher that the cases appeared in the following two bins (10000000-20000000 and 20000000- 30000000). It means that for both entire population and random sample, most of the films have a gross value in the range of 0-10000000.
- If not consider the points on the far right, variation for entire population is at 0 to 200000000, and for the random sample is at from 0 to 80000000. The random sample has less variation than the entire population.
- Although with different number of data points, the shape of the histograms of entire population and the random sample looks roughly similar. Both have more cases with lower gross values and less cases with higher gross values, and both have some outliers on the far right. Both are unsymmetrical. The right skewed distribution is further confirmed by the descriptive statics that both datasets have much larger mean than median as well as the shape of box-and-whisker plot (longer upper whisker).
- For the entire population, there seem to be two possible outliers at 240000000-250000000 and 300000000-310000000. It is later revealed by box-and-whisker plot that the outliers are “Independence_Day” and “Twister”. For the random sample, one possible outlier is at 100000000-110000000. It is later revealed by box-and-whisker plot that the outlier is “First_Wives_Club_The” whose gross value is 105410874. Considering the scale of the box- and-whisker plot, the interquartile range of the entire sample (30283674) is larger than that of the random sample (24994205). It is aligned with previous conclusion that the random sample has less variation than the entire population.
