How many rookies received a rating of 4 or better
Fifty pro-football rookies were rated on a scale of 1 to 5, based on performance at a training camp as well as on past performance. A ranking of 1 indicated a poor prospect, whereas a ranking of 5 indicated an excellent prospect. The following frequency distribution was constructed.
Rating Frequency
1 4
2 10
3 14
4 18
5 4
a.) How many of the rookies received a rating of 4 or better? How many of the rookies received a rating of 2 or worse?
- The rookies who received a rating of 4+ are 22 and the ones who received a rating of 2 or worse are 14.
b.) Construct the relative frequency distribution. What proportion received a rating of 5?
-
c.) Construct a bar chart. Comment on the findings.
a.) To determine how many rookies received a rating of 4 or better, we add up the frequencies for ratings 4 and 5: 18 + 4 = 22. Therefore, 22 rookies received a rating of 4 or better.
To determine how many rookies received a rating of 2 or worse, we add up the frequencies for ratings 1 and 2: 4 + 10 = 14. Therefore, 14 rookies received a rating of 2 or worse.
b.) To construct the relative frequency distribution, we divide the frequency for each rating by the total number of rookies (50). The relative frequency for each rating is as follows:
Rating Frequency Relative Frequency 1 4 4/50 = 0.08 2 10 10/50 = 0.20 3 14 14/50 = 0.28 4 18 18/50 = 0.36 5 4 4/50 = 0.08
Therefore, the proportion of rookies who received a rating of 5 is 4/50 = 0.08 (or 8%).
c.) To construct a bar chart, we can represent each rating on the x-axis and the frequency or relative frequency on the y-axis. The height of each bar will correspond to the frequency or relative frequency for each rating.
Based on the given data, the bar chart will look like this:
Frequency
| *
| *
| *
| *
| * *
| * *
| * * *
| * * * *
| * * * *
-----------------------
1 2 3 4 5
From the bar chart, we can observe that the majority of rookies received ratings of 3 or higher, with the highest frequency at rating 4. However, there are only a few rookies who received ratings of 1 or 5.