Question

In a statistics class, 10 scores were randomly selected with the following results: 74, 73, 77, 77, 71, 68, 65, 77, 67, 66. What is the 65th percentile?

Answer 1

Answer:The 65th percentile is 74

Explanation:

The total number of scores sampled is 10. So n = 10

We want to determine the 65th percentile. First step is to rearrange the scores in an increasing order. It becomes

65, 66, 67, 68, 71, 73, 74, 77, 77, 77

Next step is to determine the index by multiplying 65% by n. It becomes

65/100×10 = 6.5. Rounding up to the nearest whole number, it becomes 7

The 65th percentile will be the 7th term from the left. It becomes

74

Answer 2

The 65th percentile is between 73 and 74

Explanation:

Rearrange the ungrouped data in ascending order: 65,66,67,68,71,73,74,77,77,77

The 65th percentile is 65/100 of N ( N = 10) = 65/100 × 10 = 6.5

The 65th percentile is the 6.5th term. The 6th term is 73 and the 7th term is 74, the 6.5th term is between the 6th and 7th term

The 65th percentile is between 73 and 74