Sure, I would be glad to explain how to solve the problem step-by-step using the given dataset [tex]\( \{70, 63, 67, 62, 63\} \)[/tex].
### 1. Ordering the Data
First, let's put the dataset in ascending order:
[tex]\[ \{62, 63, 63, 67, 70\} \][/tex]
### 2. Mean
The mean (average) is calculated by summing all the data points and then dividing by the number of data points.
[tex]\[ \text{Sum of data points} = 70 + 63 + 67 + 62 + 63 = 325 \][/tex]
[tex]\[ \text{Number of data points} = 5 \][/tex]
[tex]\[ \text{Mean} = \frac{325}{5} = 65.0 \][/tex]
### 3. Median
The median is the middle value when the data set is ordered from least to greatest. If there is an odd number of observations, the median is the middle number. If there is an even number of observations, the median is the average of the two middle numbers.
Since there are 5 data points (an odd number), the median is the 3rd value in the ordered list:
[tex]\[ \{62, 63, 63, 67, 70\} \][/tex]
So, the median is:
[tex]\[ \text{Median} = 63 \][/tex]
### 4. Mode
The mode is the value that appears most frequently in the dataset.
In the ordered dataset [tex]\( \{62, 63, 63, 67, 70\} \)[/tex], the value 63 appears twice, which is more frequently than any other number.
Therefore, the mode is:
[tex]\[ \text{Mode} = 63 \][/tex]
### 5. Range
The range is the difference between the highest and lowest values in the dataset.
[tex]\[ \text{Maximum value} = 70 \][/tex]
[tex]\[ \text{Minimum value} = 62 \][/tex]
[tex]\[ \text{Range} = 70 - 62 = 8 \][/tex]
### Final Summary
- Mean: 65.0
- Median: 63
- Mode: 63
- Range: 8
Therefore, by following these steps, we have calculated that the mean is 65.0, the median is 63, the mode is 63, and the range is 8 for the given dataset [tex]\( \{70, 63, 67, 62, 63\} \)[/tex].
