The scores of 20 students in a Math quiz are as follows:
25, 33, 35, 45, 34, 26, 29, 35, 38, 40, 45, 38, 28, 29, 25, 39, 32, 37, 47, 45
Calculate the mean, median, and mode of these scores.
Answer (2)
The mean of the scores is 37.4, the median is 36, and the mode is 45. These values summarize the distribution of students' scores in the Math quiz. By following the steps to calculate each measure, we can understand the typical performance of the students.
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To find the mean, median, and mode of the given scores, follow these steps:
Mean : The mean is the average of all the scores. To calculate it, sum all the scores and then divide by the number of scores.
Mean = 20 25 + 33 + 35 + 45 + 34 + 26 + 29 + 35 + 38 + 40 + 45 + 38 + 28 + 29 + 25 + 39 + 32 + 37 + 47 + 45
First, sum the scores:
25 + 33 + 35 + 45 + 34 + 26 + 29 + 35 + 38 + 40 + 45 + 38 + 28 + 29 + 25 + 39 + 32 + 37 + 47 + 45 = 670
Then, divide by 20:
Mean = 20 670 = 33.5
Median : The median is the middle score when all scores are arranged in increasing order. If there is an even number of scores, the median is the average of the two middle numbers.
First, arrange the scores:
25 , 25 , 26 , 28 , 29 , 29 , 32 , 33 , 34 , 35 , 35 , 37 , 38 , 38 , 39 , 40 , 45 , 45 , 45 , 47
Since there are 20 scores, the median is the average of the 10th and 11th scores.
The 10th score is 35 and the 11th score is 35.
Median = 2 35 + 35 = 35
Mode : The mode is the number that appears most frequently. Look for the score(s) with the highest frequency.
In this set:
25 appears 2 times
29 appears 2 times
35 appears 2 times
38 appears 2 times
45 appears 3 times
Therefore, the mode is 45, as it appears the most frequently.
Summary :
Mean : 33.5
Median : 35
Mode : 45
