Thank you for visiting The following questions refer to the given data set Data Set 71 6 61 3 70 2 86 8 88 4 103 8 103 8. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
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
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Rewritten by : Jeany
