From science to arts, IDNLearn.com has the answers to all your questions. Get accurate answers to your questions from our community of experts who are always ready to provide timely and relevant solutions.
Sagot :
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!
### 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!
We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Thank you for trusting IDNLearn.com with your questions. Visit us again for clear, concise, and accurate answers.
