Question

a) Suppose that the academic standings of students in a programming competition in your investigation ( is as follows: freshman n = 25, junior n = 20, sophomore, n = 22, senior n = 15, graduate n = 10.

i) Construct a frequency distribution for these data.
ii) On what measurement scale are these observations?
iii) Does it matter in what order we arrange the categories?

Answer 1

[AI-generated answer — Bot GPT 3.5]

i) Frequency distribution:

Freshman: 25
Junior: 20
Sophomore: 22
Senior: 15
Graduate: 10

ii) These observations are on a nominal measurement scale, as they represent categories without a natural order or ranking.

iii) It does not matter in what order we arrange the categories as long as each category is clearly defined and mutually exclusive. The frequency distribution will remain the same regardless of the order of the categories.

Answer 2

c) What is percentile and percentile rank? Based on the notion of percentile and percentile rank.

ii) Can a percentile have the value 517? Explain.
ii. Can a percentile have the value -5.8? Explain.
iii) Can a percentile rank have the value of 517? Explain.
iv. Can a percentile rank have the value of -5.8? Explain

Answer 3

[AI-generated answer — Bot GPT 3.5]

i) Percentile is a measure that indicates the value below which a given percentage of observations in a group of observations fall. For example, if a student scored at the 80th percentile on a test, it means that they scored higher than 80% of the other students.

Percentile rank, on the other hand, is the percentage of scores that fall at or below a given score. For example, if a student's score is at the 80th percentile rank, it means that their score is higher than 80% of the other scores.

ii) A percentile is always a value between 0 and 100, representing a percentage. Therefore, a percentile cannot have a value of 517 because it exceeds the maximum value of 100%.

iii) Similarly, a percentile cannot have a negative value like -5.8 because it must represent a positive percentage rank.

iv) A percentile rank is a value between 0 and 100, representing the percentage of scores that fall at or below a given score. It cannot have a value of 517 as it exceeds the maximum value of 100%. Likewise, a percentile rank cannot have a negative value like -5.8 as it represents the percentage of scores.