Answer :
Certainly! Let's work through finding the median, mode, and mean of the data set step-by-step.
We are given the data set: 93, 84, 93, 40, 84, 91, 93, 87.
1. Median
To find the median, we need to sort the data set and then find the middle value. If there are an even number of data points, the median will be the average of the two middle numbers.
- First, let's sort the data: 40, 84, 84, 87, 91, 93, 93, 93
- There are 8 numbers in the data set, which is an even number. So, we find the median by averaging the 4th and 5th numbers in the sorted list.
- The 4th number is 87, and the 5th number is 91.
- Average of the 4th and 5th numbers: (87 + 91) / 2 = 89.0
So, the median is 89.0.
2. Mode
The mode is the number that appears most frequently in a data set.
- From the sorted data: 40, 84, 84, 87, 91, 93, 93, 93
- The number 93 appears three times, which is more frequent than any other number in the set.
So, the mode is 93.
3. Mean
The mean is the average of all numbers in the data set. It is calculated by adding up all the numbers and then dividing by the total count of numbers.
- Sum of all numbers: 93 + 84 + 93 + 40 + 84 + 91 + 93 + 87 = 665
- There are 8 numbers in the data set.
- Mean: 665 / 8 = 83.125
So, the mean is 83.125.
In summary, for the given data set:
- Median: 89.0
- Mode: 93
- Mean: 83.125
We are given the data set: 93, 84, 93, 40, 84, 91, 93, 87.
1. Median
To find the median, we need to sort the data set and then find the middle value. If there are an even number of data points, the median will be the average of the two middle numbers.
- First, let's sort the data: 40, 84, 84, 87, 91, 93, 93, 93
- There are 8 numbers in the data set, which is an even number. So, we find the median by averaging the 4th and 5th numbers in the sorted list.
- The 4th number is 87, and the 5th number is 91.
- Average of the 4th and 5th numbers: (87 + 91) / 2 = 89.0
So, the median is 89.0.
2. Mode
The mode is the number that appears most frequently in a data set.
- From the sorted data: 40, 84, 84, 87, 91, 93, 93, 93
- The number 93 appears three times, which is more frequent than any other number in the set.
So, the mode is 93.
3. Mean
The mean is the average of all numbers in the data set. It is calculated by adding up all the numbers and then dividing by the total count of numbers.
- Sum of all numbers: 93 + 84 + 93 + 40 + 84 + 91 + 93 + 87 = 665
- There are 8 numbers in the data set.
- Mean: 665 / 8 = 83.125
So, the mean is 83.125.
In summary, for the given data set:
- Median: 89.0
- Mode: 93
- Mean: 83.125
