Answer :
To find the arithmetic mean, median, and mode of the given data set, let’s go through each step-by-step:
Arithmetic Mean:
The arithmetic mean, or average, is calculated by adding up all the values in the data set and then dividing by the number of values.
Given data set: 71.6, 61.3, 70.2, 86.8, 88.4, 103.8, 103.8, 103.8, 99.8, 83.
First, add all the numbers together:
[tex]71.6 + 61.3 + 70.2 + 86.8 + 88.4 + 103.8 + 103.8 + 103.8 + 99.8 + 83 = 872.5[/tex]
Next, divide the sum by the number of data points, which is 10:
[tex]\text{Mean} = \frac{872.5}{10} = 87.25[/tex]
Median:
The median is the middle number in a sorted, ascending or descending, list of numbers.
First, sort the numbers in ascending order:
61.3, 70.2, 71.6, 83, 86.8, 88.4, 99.8, 103.8, 103.8, 103.8.
Since there are 10 numbers, the median will be the average of the 5th and 6th values.
5th value: 86.8, 6th value: 88.4
Median [tex]= \frac{86.8 + 88.4}{2} = \frac{175.2}{2} = 87.6[/tex]
Mode:
The mode is the number that occurs most frequently in a data set.
In this data set, 103.8 appears three times, more frequently than any other number.
Therefore, the mode is 103.8.
In summary, for the given data set:
- Mean = 87.25
- Median = 87.6
- Mode = 103.8