Sure, let's calculate the mean, median, mode, and range for each data set step-by-step.
### Data Set 1: [7, 18, 3, 6, 8, 7]
1. Mean:
[tex]\[
\text{Mean} = \frac{\sum \text{of all values}}{\text{number of values}} = \frac{7 + 18 + 3 + 6 + 8 + 7}{6} = \frac{49}{6} \approx 8.17
\][/tex]
2. Median:
First, we sort the data: [3, 6, 7, 7, 8, 18]. Since there is an even number of observations, the median is the average of the two middle numbers (7 and 7):
[tex]\[
\text{Median} = \frac{7 + 7}{2} = 7
\][/tex]
3. Mode:
The mode is the number that appears most frequently:
[tex]\[
\text{Mode} = 7 \quad (\text{appears twice})
\][/tex]
4. Range:
The range is the difference between the highest and lowest values:
[tex]\[
\text{Range} = 18 - 3 = 15
\][/tex]
### Data Set 2: [15, 15, 14, 14, 10, 9, 13, 11]
1. Mean:
[tex]\[
\text{Mean} = \frac{15 + 15 + 14 + 14 + 10 + 9 + 13 + 11}{8} = \frac{101}{8} = 12.625
\][/tex]
2. Median:
First, we sort the data: [9, 10, 11, 13, 14, 14, 15, 15]. With an even number of observations, the median is the average of the two middle numbers (13 and 14):
[tex]\[
\text{Median} = \frac{13 + 14}{2} = 13.5
\][/tex]
3. Mode:
The mode is the number that appears most frequently:
[tex]\[
\text{Mode} = 14 \quad \text{and} \quad 15 \quad (\text{each appears twice})
\][/tex]
4. Range:
[tex]\[
\text{Range} = 15 - 9 = 6
\][/tex]
### Data Set 3: [59, 52, 57, 44, 46, 48, 41, 57, 47]
1. Mean:
[tex]\[
\text{Mean} = \frac{59 + 52 + 57 + 44 + 46 + 48 + 41 + 57 + 47}{9} = \frac{451}{9} = 50.11
\][/tex]
2. Median:
First, we sort the data: [41, 44, 46, 47, 48, 52, 57, 57, 59]. Since there is an odd number of observations, the median is the middle number:
[tex]\[
\text{Median} = 48
\][/tex]
3. Mode:
The mode is the number that appears most frequently:
[tex]\[
\text{Mode} = 57 \quad (\text{appears twice})
\][/tex]
4. Range:
[tex]\[
\text{Range} = 59 - 41 = 18
\][/tex]
### Data Set 4: [80, 82, 82, 83, 87, 81, 83, 92, 80, 89]
1. Mean:
[tex]\[
\text{Mean} = \frac{80 + 82 + 82 + 83 + 87 + 81 + 83 + 92 + 80 + 89}{10} = \frac{839}{10} = 83.9
\][/tex]
2. Median:
First, we sort the data: [80, 80, 81, 82, 82, 83, 83, 87, 89, 92]. With an even number of observations, the median is the average of the two middle numbers (82 and 83):
[tex]\[
\text{Median} = \frac{82 + 83}{2} = 82.5
\][/tex]
3. Mode:
The mode is the number that appears most frequently:
[tex]\[
\text{Mode} = 80 \quad \text{and} \quad 82 \quad \text{and} \quad 83 \quad (\text{each appear twice})
\][/tex]
4. Range:
[tex]\[
\text{Range} = 92 - 80 = 12
\][/tex]
I hope this detailed breakdown helps you understand how to calculate the mean, median, mode, and range for different sets of data!
