the 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 mod of the data set?
Mean: To find the mean, we add up all the scores and divide by the total number of scores.
83 + 85 + 82 + 93 + 83 + 84 + 95 + 87 + 86 + 94 = 872
Mean = 872/10 = 87.2
Median: To find the median, we need to find the middle value when the scores are listed in order.
82, 83, 83, 84, 85, 86, 87, 93, 94, 95
The median is 85.5, which is the average of the middle two values (85 and 86).
Mode: The mode is the score that appears most frequently in the data set. In this case, there are two values that appear twice (83 and 94), while all other scores only appear once. Therefore, there is no single mode for this data set.
To find the mean, median, and mode for the given data set, follow these steps:
Step 1: Order the Data Set
Order the data set in ascending order: 82, 83, 83, 84, 85, 86, 87, 93, 94, 95
Step 2: Calculate the Mean
The formula to calculate the mean (average) is:
Mean = Sum of all numbers / Total number of numbers
Mean = (82 + 83 + 83 + 84 + 85 + 86 + 87 + 93 + 94 + 95) / 10
Mean = 872 / 10
Mean = 87.2
So, the mean of the data set is 87.2.
Step 3: Find the Median
To find the median, we need to determine the middle value. Since we have 10 numbers in the data set, the median will be the average of the fifth and sixth numbers.
Median = (85 + 86) / 2
Median = 171 / 2
Median = 85.5
So, the median of the data set is 85.5.
Step 4: Identify the Mode
The mode is the number that appears most frequently in the data set. In this case, the data set does not have a mode as no number appears more than once.
Therefore, the mode of the data set is "no mode."
In summary, the mean of the data set is 87.2, the median is 85.5, and the mode is "no mode" as there are no repeated numbers.