Explain whether there are any outliers in these data or not. The 5-number summary for the run times in minutes of the 150 highest grossing movies of 2010 is provided.

Explain whether there are any outliers in these data or not.
The 5-number summary for the run times in minutes of the 150 highest grossing movies of 2010 is provided.

Answers (1)

Inter quartile range:
In contrast to the range, which measures only differences between the extremes, the inter quartile range (also called mid spread) is the difference between the third quartile and the first quartile. Thus, it measures the variation in the middle 50 percent of the data, and, unlike the range, is not affected by extreme values. \(IQR = Q_{3} - Q_{1}\),
From the given 5-number summary for the run times in minutes \(Q_{1} = 98\ and\ Q_{3} = 116\).
\(IQR = Q_{3} - Q_{1}\)
\(= 116-98=18\)
Thus, the interquartile range is 18.
Outlier Rule:
If any observation is greater than \(Q_{3} + 1.5\) IQR or less than \(Q_{1} — 1.5\) IQR then that observation is considered as high or low outlier.
\(Upper fence = Q_{3} + 1.5\) IQR
\(= 116 + 1.5(18)= 116+27= 143\)
Here the maximum value 160 which is greater than the upper fence 143. Hence 160 is considered as the higher outlier.
\(Lower fence = Q_{1} — 1.5/\)IQR
\(= 98 — 1.5(18)\)
\(= 98-27=71\)
Here the minimum value 43 which is below the lower fence 71. Hence, 43 is considered as the low outlier.
Thus, there is a high and a low outlier in these data.

Relevant Questions

asked 2020-10-23
The table below shows the number of people for three different race groups who were shot by police that were either armed or unarmed. These values are very close to the exact numbers. They have been changed slightly for each student to get a unique problem.
Suspect was Armed:
Black - 543
White - 1176
Hispanic - 378
Total - 2097
Suspect was unarmed:
Black - 60
White - 67
Hispanic - 38
Total - 165
Black - 603
White - 1243
Hispanic - 416
Total - 2262
Give your answer as a decimal to at least three decimal places.
a) What percent are Black?
b) What percent are Unarmed?
c) In order for two variables to be Independent of each other, the P \((A and B) = P(A) \cdot P(B) P(A and B) = P(A) \cdot P(B).\)
This just means that the percentage of times that both things happen equals the individual percentages multiplied together (Only if they are Independent of each other).
Therefore, if a person's race is independent of whether they were killed being unarmed then the percentage of black people that are killed while being unarmed should equal the percentage of blacks times the percentage of Unarmed. Let's check this. Multiply your answer to part a (percentage of blacks) by your answer to part b (percentage of unarmed).
Remember, the previous answer is only correct if the variables are Independent.
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If answer c is "significantly different" than answer d, then that means that there could be a different percentage of unarmed people being shot based on race. We will check this out later in the course.
Let's compare the percentage of unarmed shot for each race.
e) What percent are White and Unarmed?
f) What percent are Hispanic and Unarmed?
If you compare answers d, e and f it shows the highest percentage of unarmed people being shot is most likely white.
Why is that?
This is because there are more white people in the United States than any other race and therefore there are likely to be more white people in the table. Since there are more white people in the table, there most likely would be more white and unarmed people shot by police than any other race. This pulls the percentage of white and unarmed up. In addition, there most likely would be more white and armed shot by police. All the percentages for white people would be higher, because there are more white people. For example, the table contains very few Hispanic people, and the percentage of people in the table that were Hispanic and unarmed is the lowest percentage.
Think of it this way. If you went to a college that was 90% female and 10% male, then females would most likely have the highest percentage of A grades. They would also most likely have the highest percentage of B, C, D and F grades
The correct way to compare is "conditional probability". Conditional probability is getting the probability of something happening, given we are dealing with just the people in a particular group.
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h) What percent of whites shot and killed by police were unarmed?
i) What percent of Hispanics shot and killed by police were unarmed?
You can see by the answers to part g and h, that the percentage of blacks that were unarmed and killed by police is approximately twice that of whites that were unarmed and killed by police.
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