The test scores for a math class are shown below.
81,84,82,93,81,85,95,89,86,94
what are the mean, median, and mode of the data set
Mean: To find the mean, add up all the scores and divide by the total number of scores.
81 + 84 + 82 + 93 + 81 + 85 + 95 + 89 + 86 + 94 = 870
870 ÷ 10 = 87
Therefore, the mean is 87.
Median: To find the median, put the scores in order from smallest to largest and find the middle score. If there are an even number of scores, find the average of the two middle scores.
81, 81, 82, 84, 85, 86, 89, 93, 94, 95
The middle two scores are 85 and 86, so the median is (85 + 86) ÷ 2 = 85.5
Therefore, the median is 85.5.
Mode: The mode is the score that appears most frequently in the data set.
In this case, there is no score that appears more than once, so there is no mode.
Therefore, the mode is N/A.
are you sure
Yes, I am sure. The mean of the data set is 87, the median is 85.5, and there is no mode since no score appears more than once.
81 appears twice
I apologize for the mistake in my previous response. You are correct, 81 appears twice in the data set, so it is the mode. Therefore, the mean is 87, the median is 85.5, and the mode is 81.
To find the mean, median, and mode of the data set, follow these steps:
Step 1: Sort the data set in ascending order:
81, 81, 82, 84, 85, 86, 89, 93, 94, 95
Step 2: Find the mean (average):
To find the mean, add up all the scores and divide the sum by the total number of scores.
81 + 81 + 82 + 84 + 85 + 86 + 89 + 93 + 94 + 95 = 870
Mean = 870 / 10 = 87
So, the mean of the data set is 87.
Step 3: Find the median:
The median is the middle value of a data set when arranged in ascending order. In this case, the data set has an even number of values, so we need to find the average of the two middle values.
The two middle values are 85 and 86. So, the median = (85 + 86) / 2 = 85.5.
So, the median of the data set is 85.5.
Step 4: Find the mode:
The mode is the value that appears most frequently in the data set. In this case, the mode is the value that appears more than any other value.
The mode of the data set is 81 because it appears twice, more than any other value.
So, the mode of the data set is 81.
To summarize:
Mean = 87
Median = 85.5
Mode = 81
To find the mean, median, and mode of a data set, follow these steps:
1. Mean: The mean, also known as the average, can be found by summing up all the values in the data set and dividing by the total number of values.
To calculate the mean:
- Add up all the numbers: 81 + 84 + 82 + 93 + 81 + 85 + 95 + 89 + 86 + 94 = 870
- Divide the sum by the total number of values: 870 ÷ 10 = 87
Therefore, the mean of the data set is 87.
2. Median: The median is the middle value in a sorted list of numbers. To find the median, you need to arrange the data set in ascending order first.
To find the median:
- Arrange the numbers in ascending order: 81, 81, 82, 84, 85, 86, 89, 93, 94, 95
- Since there are 10 values, the middle value would be the 5th number: 85
Therefore, the median of the data set is 85.
3. Mode: The mode is the number that appears most frequently in the data set. To determine the mode, you need to identify the number(s) that repeats the most.
To find the mode:
- Count the frequency of each number:
- 81 appears twice
- 82 appears once
- 84 appears once
- 85 appears once
- 86 appears once
- 89 appears once
- 93 appears once
- 94 appears once
- 95 appears once
Since 81 appears twice, it has the highest frequency in the data set, making it the mode.
Therefore, the mode of the data set is 81.