Sure, let's calculate the mean, median, and mode of the dataset [tex]\(\{23, 65, 56, 56, 56, 56\}\)[/tex] step by step.
### Mean
The mean (or average) is calculated by summing all the numbers in the dataset and then dividing by the number of elements in the dataset.
1. First, sum all the elements:
[tex]\[
23 + 65 + 56 + 56 + 56 + 56 = 312
\][/tex]
2. Count the number of elements in the dataset:
[tex]\[
6
\][/tex]
3. Calculate the mean:
[tex]\[
\text{Mean} = \frac{312}{6} = 52
\][/tex]
### Median
The median is the middle value of a dataset that has been arranged in ascending order. If the dataset has an even number of elements, the median is the average of the two middle numbers.
1. Arrange the dataset in ascending order:
[tex]\[
23, 56, 56, 56, 56, 65
\][/tex]
2. Since there are 6 elements (an even number), the median is the average of the 3rd and 4th elements:
[tex]\[
\text{Median} = \frac{56 + 56}{2} = 56
\][/tex]
### Mode
The mode is the value that appears most frequently in the dataset.
1. Identify the most frequent value(s):
- [tex]\(23\)[/tex] appears once
- [tex]\(65\)[/tex] appears once
- [tex]\(56\)[/tex] appears four times
2. Clearly, [tex]\(56\)[/tex] appears the most frequently.
[tex]\[
\text{Mode} = 56
\][/tex]
### Summary
[tex]\[
\text{Mean} = 52, \quad \text{Median} = 56, \quad \text{Mode} = 56
\][/tex]
