Let's address each part of the question in detail based on the provided data.
### a. Which score frequently appears?
To find the most frequently occurring score (the mode), we need to look at the frequency of each score in the dataset.
Here are the scores again:
24, 19, 19, 23, 27,
25, 14, 23, 20, 25,
21, 18, 17, 23, 24,
23, 19, 23, 28, 23
We observe the number of times each score appears:
- 23 appears 7 times
- 19 appears 3 times
- 24 and 25 appear 2 times each
- All other scores (14, 17, 18, 20, 21, 27, 28) appear 1 time each.
Thus, the mode, or the most frequently occurring score, is 23.
### b. What score is the typical score of the group? Why?
To find the typical score, we use the mean (average) of the scores. The mean is calculated by summing up all the scores and then dividing by the number of scores.
First, sum all the scores:
24 + 19 + 19 + 23 + 27 + 25 + 14 + 23 + 20 + 25 + 21 + 18 + 17 + 23 + 24 + 23 + 19 + 23 + 28 + 23 = 438
Next, divide this sum by the number of scores (20):
[tex]\[ \text{Mean} = \frac{438}{20} = 21.9 \][/tex]
Therefore, the typical score of the group, which is the mean, is 21.9.
### c. What score appear to be the median? How many learners fall below that score?
To find the median, we need to sort the scores in ascending order and then find the middle score. If the number of scores is even, the median is the average of the two middle numbers.
Here are the ordered scores:
14, 17, 18, 19, 19, 19, 20, 21, 23, 23, 23, 23, 23, 24, 24, 25, 25, 27, 28
Since there are 20 scores, the median is the average of the 10th and 11th scores:
[tex]\[ \text{Median} = \frac{23 + 23}{2} = 23 \][/tex]
Thus, the median score is 23.
Next, we count the number of learners who scored below the median. These learners scored:
14, 17, 18, 19, 19, 19, 20, 21
There are [tex]\(8\)[/tex] scores below the median.
### Summary
a. The most frequently appearing score is 23.
b. The typical score (mean) is 21.9.
c. The median score is 23, and there are 8 learners who scored below the median.
