Question 1184641: For the following distribution of scores:
x f
10 1
9 2
8 4
7 5
6 3
5 1
4 1
3 1
a) Find the middle 30% of the scores.
b) Find the bottom 20% of the scores.
c) Find the top 10% of the scores.
d) Find the bottom 70% of the scores.
e) Find the top 60% of the scores.
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here's how to find the requested percentiles for the given distribution:
First, let's calculate the cumulative frequencies:
| x | f | Cumulative f |
| --- | --- | ------------- |
| 10 | 1 | 1 |
| 9 | 2 | 3 |
| 8 | 4 | 7 |
| 7 | 5 | 12 |
| 6 | 3 | 15 |
| 5 | 1 | 16 |
| 4 | 1 | 17 |
| 3 | 1 | 18 |
The total number of scores is 18.
**a) Middle 30%:**
* The middle 30% is the range from the 35th percentile to the 65th percentile.
* 35th percentile: 0.35 * 18 = 6.3. The 7th score is 8, so the 35th percentile is approximately 8.
* 65th percentile: 0.65 * 18 = 11.7. The 12th score is 7, so the 65th percentile is approximately 7.
* The middle 30% of the scores are 7 and 8.
**b) Bottom 20%:**
* 20th percentile: 0.20 * 18 = 3.6. The 4th score is 8, so the 20th percentile is approximately 8.
* The bottom 20% of the scores are 8 and below.
**c) Top 10%:**
* 90th percentile: 0.90 * 18 = 16.2. The 17th score is 4, so the 90th percentile is approximately 4.
* The top 10% of the scores are 4 and above.
**d) Bottom 70%:**
* 70th percentile: 0.70 * 18 = 12.6. The 13th score is 7, so the 70th percentile is approximately 7.
* The bottom 70% of the scores are 7 and below.
**e) Top 60%:**
* 40th percentile: 0.40 * 18 = 7.2. The 8th score is 8, so the 40th percentile is approximately 8.
* The top 60% of the scores are 8 and above.
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