Question

Variable Mean Median Q1 Q3 Two-Star 65.08 69.50 46.50 79.25 Three-Star 89.74 87.00 70.75 107.00 Four-Star 127.74 125.50 90.75 150.00 B. Variable Range Interquartile Range Variance Standard deviation Coefficient of variation Two - star 94.00 32.75 473.80 21.77 33.45 Three-star 126.00 36.25 761.66 27.60 30.75 Four-star 134.00 59.25 1583.60 39.79 31.15 Based on the results, what conclusions can you reach concerning these variables?

Answer 1

The data given is -

Variable	Mean	Median	Q1	Q3
Two-Star	65.08	69.5	46.5	79.25
Three-Star	89.74	87	70.75	107
Four-Star	127.74	125.5	90.75	150
	Range	Interquartile Range	Variance	Standard Deviation	Coefficient of Variation
Two-Star	94	32.75	473.8	21.77	33.45
Three-Star	126	36.25	761.66	27.6	30.75
Four-Star	134	59.25	1583.6	39.79	31.15

We can clearly see that the mean of variable 'Two-star ' is least while its maximum for the variable 'Four-Star'. The variable 'Three-Star' has mean in between these variables.

The median of the 'Two-start' variable is to the right of mean while for the 'Three-Star' and 'Four-Star', the median is to the left of mean. It means that the 'Two-Star' variable has left-skewed distribution while the other two have right skewed distribution.

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Now note that the range of variable 'Two-Star' is least but there is not much difference between the range of 'Three-Star' and 'Four'Star' variables. Which indicates that the linear spread of the three-star variable and the four-star variable are similar. But the variance of four-star variable is almost twice to that of three-star variable.

Which means there is a lot of fluctuation in the 'four-star' variable which results in such high variance.