Listed are 32 ages for Academy Award winning best actors in order from smallest to largest. (Round your answers to the nearest whole number.) 18; 18; 21; 22; 25; 26; 27; 29; 30; 31; 31; 33; 36; 37; 37; 41; 42; 47; 52; 55; 57; 58; 62; 64; 67; 69; 71; 72; 73; 74; 76; 77

(a) Find the percentile of 37. th percentile
(b) Find the percentile of 72. th percentile

Answer:

a) 37th percentile: 33 years

b) 72nd percentile: 62 years

Step-by-step explanation:

The kth percentile divides the data into two: on the one hand the lowest k% of the data, and on the other the (1-k)% higher of the data.

For the list provided, the 37th percentile falls to the age of 33. This means that 37% of the data are for ages under 33 years.

The 72nd percentile falls at the age of 62 (72% of the ages fall below 62 years).

AGE PERCENTILE

18 6%

21 9%

22 13%

25 16%

26 19%

27 22%

29 25%

30 28%

31 34%

33 38%

36 41%

37 47%

41 50%

42 53%

47 56%

52 59%

55 63%

57 66%

58 69%

62 72%

64 75%

67 78%

69 81%

71 84%

72 88%

73 91%

74 94%

76 97%

77 100%

Final answer:

The percentile rank of 37 among Academy Award-winning best actors is the 45th percentile, and the percentile rank of 72 is the 87th percentile. These are determined by their positions in the ordered list and the total number of ages listed.

Explanation:

Finding the Percentiles of Ages for Academy Award-winning Best Actors

To find the percentile for a given age in a sorted list, use the formula:

Percentile Rank = (Number of values below your score + 0.5) / Total number of scores x 100

a. To find the percentile of 37 from the list of ages, we must first locate 37 within the ordered list. There are two values of 37, so we use the position of the second 37 for our calculation since it is the last occurrence of that value. This position is 15th in the list. Using the percentile rank formula, we calculate:

Percentile Rank of 37 = (14 + 0.5) / 32 x 100 = 45th percentile (rounded to the nearest whole number).

b. To find the percentile of 72, we find the position of 72, which is 28th in the list. Using the same formula:

Percentile Rank of 72 = (27 + 0.5) / 32 x 100 = 87th percentile (rounded to the nearest whole number).

Therefore, an actor who won the Academy Award at age 37 would be in the 45th percentile of ages of all such actors, while an actor who won at age 72 would be in the 87th percentile.