Test scores of average 7th grade class are: 77,83,92,66,89,74,98,79,85,75,80,88,76,96,84,100,71,93,70,82
The mean is 82.9 and the standard deviaition is 9.7
1. What score is in the 80th percentile?
2. Your teacher tells you that your score beat 78% of the scores on the test. What was your score?
arrange the scores in order.
The 80th %ile is that score above 80% of the others.
Your score is the 78th %ile, so it should be close to the score found above.
what a 66 in 7th grade is
To find the score in the 80th percentile and determine your score if it beats 78% of the scores, we need to use the concept of percentiles.
1. To find the score in the 80th percentile:
- First, sort the given test scores in ascending order: 66, 70, 71, 74, 75, 76, 77, 79, 80, 82, 83, 84, 85, 88, 89, 92, 93, 96, 98, 100.
- Calculate the index corresponding to the 80th percentile using the formula: p = (percentile / 100) * (n + 1), where p is the index, percentile is 80, and n is the total number of scores (20 in this case). So, p = (80 / 100) * (20 + 1) = 16.2.
- The score at the 16th index is 88, and the score at the 17th index is 89. Since the index 16.2 lies between these two scores, we can use interpolation to estimate the score in the 80th percentile.
- Interpolation formula: Estimated score = lower score + (difference of scores) * (decimal part of the index).
- Estimated score = 88 + (89 - 88) * 0.2 = 88 + 1 * 0.2 = 88.2.
- Therefore, the score in the 80th percentile is approximately 88.2.
2. To determine your score if it beats 78% of the scores:
- If your score beats 78% of the scores, it means that it falls in the 78th percentile.
- Follow the same steps as in the previous calculation, but this time use the percentile of 78.
- Using the interpolation formula, you can estimate your score based on the lower and upper scores around the corresponding index.
- Use the same formula as in step 1, but this time p = (78 / 100) * (20 + 1) = 15.78.
- The score at the 15th index is 85, and the score at the 16th index is 88. Since the index 15.78 lies in between these two scores, plug the values into the interpolation formula:
- Estimated score = 85 + (88 - 85) * 0.78 = 85 + 3 * 0.78 = 85 + 2.34 = 87.34.
- Therefore, your score, which beats 78% of the scores, is approximately 87.34.