Maria has the following scores on exams in her social studies class: 86, 75, 97, 58, 94, and 58.
Find the mean, median, and mode of the scores.
Should Maria’s social studies teacher use the mean, median, or mode of the exam scores to convince Maria that she needs to study more regularly for her exams? short answer
Mean:
To find the mean, you need to add up all the scores and divide by the total number of scores:
(86 + 75 + 97 + 58 + 94 + 58) / 6 = 78.0
So the mean score is 78.0.
Median:
To find the median, you need to put the scores in order from lowest to highest:
58, 58, 75, 86, 94, 97
The median is the middle score, so in this case it is 86.
Mode:
The mode is the score that appears most frequently. In this case, both 58 and 94 appear twice, so there are two modes: 58 and 94.
Based on the scores, it would be best for Maria's social studies teacher to use the mean score to convince her to study more regularly. The mean score of 78.0 indicates that Maria has room for improvement in her studying habits, as her scores are somewhat inconsistent. While the median of 86 is higher, it doesn't necessarily indicate that Maria needs to study more regularly, as it is possible to have a few low scores dragging down an otherwise good performance. Similarly, the mode doesn't give a clear indication of where Maria needs to improve.
where does the number 94 appear twice at?
I apologize for my mistake in the previous response. The number 94 appears only once in the given data set. So, there is no mode for this data set since no number occurs more than once.
but the number 58 does, so does that mean there's a mode?
Yes, you are correct. I apologize for the confusion. The number 58 appears twice in the data set, so the mode is 58. Therefore, the mode of this data set is 58.
To find the mean, add up all the scores and divide by the total number of scores:
Mean = (86 + 75 + 97 + 58 + 94 + 58) / 6 = 76.33
To find the median, we arrange the scores in order from least to greatest and find the middle value:
58, 58, 75, 86, 94, 97
Median = (75 + 86) / 2 = 80.5
To find the mode, we determine which score appears most frequently:
Mode = 58 (since it appears twice, more than any other score)
The social studies teacher can use the mean to convince Maria that she needs to study more regularly for her exams. The mean score (76.33) suggests that Maria's overall performance is below average.
To find the mean, median, and mode of Maria's exam scores, we can follow these steps:
1. Mean (Average):
To find the mean, we add up all the numbers and then divide the sum by the total number of scores. In this case, the sum of all the scores is:
86 + 75 + 97 + 58 + 94 + 58 = 468
Since there are 6 scores, we divide the sum by 6 to get the mean:
Mean = 468 / 6 = 78
2. Median:
The median is the middle number when the scores are arranged in ascending order. To find the median, we first need to sort the scores in ascending order:
58, 58, 75, 86, 94, 97
Since there are 6 scores, the middle two scores are 75 and 86. To find the median, we take the average of these two numbers:
Median = (75 + 86) / 2 = 80.5
3. Mode:
The mode is the score that occurs most frequently in the set. In this case, the score "58" occurs twice, which is more than any other score. Therefore, the mode is 58.
Now, to determine whether Maria's social studies teacher should use the mean, median, or mode to convince her to study more regularly, we need to consider the strengths and weaknesses of each measure.
- Mean: The mean reflects the average score, but it can be sensitive to extreme scores. In this case, the mean is 78, which may not accurately represent Maria's overall performance due to the low scores of 58.
- Median: The median is less affected by extreme scores and is a better representation of typical performance. In this case, the median is 80.5, closer to Maria's better-performing scores.
- Mode: The mode represents the most frequently occurring score. In this case, 58 is the mode, indicating that Maria has scored poorly multiple times.
Based on these considerations, Maria's social studies teacher should use the median (80.5) to convince her to study more regularly. The median provides a more accurate representation of her overall performance, as it is less skewed by her lower scores.