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
Mean:
To find the mean, you add up all the scores and divide by the total number of scores.
86 + 75 + 97 + 58 + 94 + 58 = 468
468 ÷ 6 = 78
The mean score is 78.
Median:
To find the median, you put the scores in order from smallest to largest and find the middle value.
58, 58, 75, 86, 94, 97
The middle values are 75 and 86. To find the median, you add those two values together and divide by two.
75 + 86 = 161
161 ÷ 2 = 80.5
The median score is 80.5.
Mode:
To find the mode, you look for the value that appears most frequently in the data set.
In this case, 58 appears twice, and all the other values appear only once.
The mode score is 58.
Based on these results, Maria's teacher should use the mean score of 78 to convince her to study more regularly. This is because the mean takes into account all the scores and is a good representation of how she is performing overall. The median and mode are also important measures of central tendency, but they can be skewed if there are extreme scores, like the 97 in this data set. Therefore, the mean is the most appropriate measure to use in this case.
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?
Based on these results, Maria's teacher should use the mean score of 78 to convince her to study more regularly. This is because the mean takes into account all the scores and is a good representation of how she is performing overall. The median and mode are also important measures of central tendency, but they can be skewed if there are extreme scores, like the 97 in this data set. Therefore, the mean is the most appropriate measure to use in this case.
To find the mean, median, and mode of the scores, follow these steps:
1. Mean: The mean is calculated by finding the sum of all the scores and dividing it by the total number of scores. So, add up all the scores:
86 + 75 + 97 + 58 + 94 + 58 = 468
Then, divide this sum by the number of scores, which is 6 (since there are 6 scores in total):
Mean = 468 / 6 = 78
So, the mean of the scores is 78.
2. Median: The median is the middle value when the scores are arranged in ascending order. To find the median, first, arrange the scores in ascending order:
58, 58, 75, 86, 94, 97
Since there are an even number of scores, take the average of the two middle scores. In this case, the two middle scores are 75 and 86. Add them together and divide by 2:
Median = (75 + 86) / 2 = 80.5
So, the median of the scores is 80.5.
3. Mode: The mode is the score that appears most frequently. From the given scores, the number 58 appears twice, while all the other scores appear only once. Therefore, the mode is 58.
Now, to answer the question of whether Maria's social studies teacher should use the mean, median, or mode to convince her to study more regularly, it depends on the specific context and purpose.
- Mean: The mean provides an average value and can be useful for overall performance assessment. However, it may be influenced by extreme values, like the high score of 97, which might not accurately represent Maria's actual performance if it's an outlier.
- Median: The median represents the middle value and is less sensitive to extreme values. It can be a better indicator of Maria's typical performance in the class.
- Mode: The mode indicates the most frequently occurring score, which may highlight areas where Maria struggles the most.
So, the teacher can use a combination of these measures to assess Maria's performance.