The data set below represents the ages of 30 executives. Which ages are above the 75th ​percentile? 424259596565464657574040565652526161555556564949666656565151626247474040494944445555414147474444292936363838424243434444Determine the values in the data set above the 75th percentile. If a data value above the 75th percentile appears more than once in the data​ set, make sure to include that value in your answer the appropriate number of times.​(Use a comma to separate answers as​ needed.)

Expert Answers

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In simpler terms, this question is asking, "arrange this group in order of increasing age, then identify the top 25% of eldest members of the group".

The ages need to be tallied, with each instance of each number counted separately. Once tallied, we can calculate an average age for the group, which will assist in giving perspective to the results (since a heavy bias toward young or old ages will skew the results and cause the top 75% of ages to grow or shrink disproportionately).

The ages tally as follows:

29x2

36x2

38x2

40x4

41x2

42x4

43x2

44x6

46x2

47x4

49x4

51x2

52x2

55x4

56x6

57x2

59x2

61x2

62x2

65x2

66x2

There are 60 individuals with ages ranging from 29 to 66. The average age is 49. The median age is 48.

There is a difficulty in identifying the 75th percentile of members by age; the 45th member of the group is part of a group of six members that are all 56 years old, so technically we have to count 56 among the top 25% despite not having more details about the exact ages of these members.

The 75th percentile begins with the three older members of the group of 56, and includes the following;

2 57 year olds

2x59

2x61

2x62

2x65

2x66

To answer the question in another perspective, the oldest 25% of ages between 29 and 66 is anyone over the age of 56.75 years, which coincides with the results above. In order to definitively answer this question, more information is needed on the group of 56 year olds.

Last Updated by eNotes Editorial on
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