Test scores for a math class are shown below.
83,85,82,93,83,84,95,87,86,94
What are the mean, median and mode of the data set?
Mean: To find the mean, we add up all the numbers and divide by the total number of scores.
83 + 85 + 82 + 93 + 83 + 84 + 95 + 87 + 86 + 94 = 872
872/10 = 87.2
The mean score is 87.2.
Median: To find the median, we need to put the scores in order from lowest to highest.
82, 83, 83, 84, 85, 86, 87, 93, 94, 95
There are 10 scores, so the median will be the average of the fifth and sixth scores.
Median = (85 + 86)/2 = 85.5
The median score is 85.5.
Mode: The mode is the score that appears most frequently. In this case, there are two scores that appear twice (83).
Therefore, the mode is 83.
To find the mean, median, and mode of the data set, follow these steps:
Step 1: Arrange the data set in ascending order:
82, 83, 83, 84, 85, 86, 87, 93, 94, 95
Step 2: Mean: Add up all the numbers in the data set and divide the sum by the total number of values:
82 + 83 + 83 + 84 + 85 + 86 + 87 + 93 + 94 + 95 = 862
The mean is 862 / 10 = 86.2
So, the mean of the data set is 86.2.
Step 3: Median: Find the middle value of the data set. Since the number of values is even (10), the median is the average of the two middle values:
The two middle values are 85 and 86.
(85 + 86) / 2 = 171 / 2 = 85.5
So, the median of the data set is 85.5.
Step 4: Mode: The mode is the value that appears most frequently in the data set:
In this data set, 83 appears twice, which is more than any other value.
So, the mode of the data set is 83.
To summarize:
Mean: 86.2
Median: 85.5
Mode: 83