Answer :
To find the mean, median, mode, and midrange of the given data set, let's look at each calculation step-by-step.
1. Mean:
The mean is the average of the data. To compute it, add up all the numbers and divide the sum by the total number of data points.
Data: 45, 82, 47, 59, 92, 70, 61, 93, 82, 57
- Sum of data = 45 + 82 + 47 + 59 + 92 + 70 + 61 + 93 + 82 + 57 = 686
- Number of data points = 10
Mean = Sum of data / Number of data points
Mean = 686 / 10 = 68.8
2. Median:
The median is the middle value of a data set when it is ordered from smallest to largest. If there is an even number of observations, the median is the average of the two middle numbers.
First, arrange the data in ascending order: 45, 47, 57, 59, 61, 70, 82, 82, 92, 93
Since there are 10 numbers (an even number), the median will be the average of the 5th and 6th numbers.
- 5th number = 61
- 6th number = 70
Median = (61 + 70) / 2 = 65.5
3. Mode:
The mode is the number that appears most frequently in the data set.
In the provided data, the number 82 appears twice, more frequently than any other number. So, the mode is 82.
4. Midrange:
The midrange is calculated as the average of the highest and lowest values in the data set.
- Minimum value = 45
- Maximum value = 93
Midrange = (Minimum value + Maximum value) / 2
Midrange = (45 + 93) / 2 = 69
Therefore, the mean is 68.8, the median is 65.5, the mode is 82, and the midrange is 69.
1. Mean:
The mean is the average of the data. To compute it, add up all the numbers and divide the sum by the total number of data points.
Data: 45, 82, 47, 59, 92, 70, 61, 93, 82, 57
- Sum of data = 45 + 82 + 47 + 59 + 92 + 70 + 61 + 93 + 82 + 57 = 686
- Number of data points = 10
Mean = Sum of data / Number of data points
Mean = 686 / 10 = 68.8
2. Median:
The median is the middle value of a data set when it is ordered from smallest to largest. If there is an even number of observations, the median is the average of the two middle numbers.
First, arrange the data in ascending order: 45, 47, 57, 59, 61, 70, 82, 82, 92, 93
Since there are 10 numbers (an even number), the median will be the average of the 5th and 6th numbers.
- 5th number = 61
- 6th number = 70
Median = (61 + 70) / 2 = 65.5
3. Mode:
The mode is the number that appears most frequently in the data set.
In the provided data, the number 82 appears twice, more frequently than any other number. So, the mode is 82.
4. Midrange:
The midrange is calculated as the average of the highest and lowest values in the data set.
- Minimum value = 45
- Maximum value = 93
Midrange = (Minimum value + Maximum value) / 2
Midrange = (45 + 93) / 2 = 69
Therefore, the mean is 68.8, the median is 65.5, the mode is 82, and the midrange is 69.
