III. The data below show the score of 20 students in the 2024 National Achievement Test (NAT). (10 pts) 35, 26, 28, 32, 21, 20, 25, 33, 35, 25, 22, 38, 35, 20, 18, 23, 21, 22, 24, 30 1. What score is typical to the group of the students? Why? 2. What score appears to be the median? How many students fall below that score? 3. Which score frequently appears?
Answer (1)
To analyze the scores of 20 students in the 2024 National Achievement Test (NAT), let's explore the typical score, median score, and the most frequently appearing score.
What score is typical to the group of students? Why?
A typical score in a dataset is often represented by the mean (average) or the median, depending on the distribution of the data. However, since we are assessing typical, it can also refer to the mode if it represents the central data better. In this case, let's calculate the mean:
Mean = 20 35 + 26 + 28 + 32 + 21 + 20 + 25 + 33 + 35 + 25 + 22 + 38 + 35 + 20 + 18 + 23 + 21 + 22 + 24 + 30
Mean = 20 465 = 23.25
The mean score is 23.25, which is around 23 or 24. However, since the data is slightly skewed by higher values like 38, the mode might be a more representative typical score.
What score appears to be the median? How many students fall below that score?
To find the median, we first sort the data in ascending order:
18, 20, 20, 21, 21, 22, 22, 23, 24, 25, 25, 26, 28, 30, 32, 33, 35, 35, 35, 38
With 20 values, the median will be the average of the 10th and 11th values:
Median = 2 25 + 25 = 25
Therefore, the median score is 25, and 9 students scored below this median (the first 9 scores in the sorted list).
Which score frequently appears?
The mode is the number that appears most frequently in a dataset. From the sorted list:
18, 20, 20, 21, 21, 22, 22, 23, 24, 25, 25, 26, 28, 30, 32, 33, 35, 35, 35, 38
The number 35 appears three times, which is more frequent than any other score.
Therefore, the mode is 35.
