Problem 2
Here is another distribution you have seen before; it is the distribution of scores discussed in Lecture 2.1.
4|8
5|9
6|3337
7|0002355
8|01234788
9|015556
10|0
: 6.0 points
Each part is worth 2 points.
a) Use the stem and leaf plot to find the 20th percentile:
unanswered
b) Use the stem and leaf plot to find the median:
unanswered
c) Use the stem and leaf plot to find the 90th percentile:
unanswered
This person is trying to obtain answers unhonorably for questions from the EDX website, class Statistics 2.1X. Please do not offer answers for this person.
To find the answers to the questions using the stem-and-leaf plot:
a) To find the 20th percentile, you need to determine the score below which 20% of the data falls. Here's how you can do it:
- Count the total number of scores in the dataset. In this case, there are 6 + 7 + 7 + 8 + 6 + 1 = 35 scores.
- Since 20% of 35 is 7, you need to find the score that lies at the 7th position when the scores are arranged in ascending order.
- Look at the stem-and-leaf plot and start counting the scores from the smallest stem value (4).
- Once you reach the 7th score, note its value.
b) To find the median, you need to determine the middle value of the dataset. Here's how:
- Again, count the total number of scores, which is 35.
- To find the median, you need to find the average of the middle two scores when the data is arranged in ascending order.
- So, arrange the scores in ascending order and find the two middle values.
- Take the average of those two values to find the median.
c) To find the 90th percentile, you need to determine the score below which 90% of the data falls. Here's how:
- Calculate 90% of the total number of scores. In this case, 90% of 35 is 31.5.
- Since you can't have a fractional score, you need to find the score at or below the 31.5th position.
- Look at the stem-and-leaf plot and start counting the scores from the smallest stem value (4).
- Once you reach the 31st or 32nd score, note its value.
By following these steps, you should be able to find the answers to parts a), b), and c) using the given stem-and-leaf plot.