Answer :
Sure! Let's find the mean, median, and mode weights of the artichokes Maria grew.
### Mean
To find the mean (average) weight, we add all the weights together and then divide by the number of weights.
List of artichoke weights:
[tex]\[ 78.8, 97.4, 54.2, 75.6, 65.7, 97.4, 83.9, 65.4, 97.4, 72.7 \][/tex]
1. Add all the weights:
[tex]\[ 78.8 + 97.4 + 54.2 + 75.6 + 65.7 + 97.4 + 83.9 + 65.4 + 97.4 + 72.7 = 788.5 \][/tex]
2. Divide by the number of weights (10 in this case):
[tex]\[ \frac{788.5}{10} = 78.85 \][/tex]
So, the mean weight of the artichokes is 78.85 grams.
### Median
To find the median, we need to arrange the weights in order and find the middle value.
1. Arrange the weights in ascending order:
[tex]\[ 54.2, 65.4, 65.7, 72.7, 75.6, 78.8, 83.9, 97.4, 97.4, 97.4 \][/tex]
2. Since there are 10 weights (an even number), the median is the average of the 5th and 6th values:
[tex]\[ \text{5th value: } 75.6, \quad \text{6th value: } 78.8 \][/tex]
3. Calculate the average of these two values:
[tex]\[ \frac{75.6 + 78.8}{2} = 77.2 \][/tex]
So, the median weight of the artichokes is 77.2 grams.
### Mode
The mode is the weight that appears most frequently.
1. Count the frequency of each weight:
[tex]\[ 78.8, 97.4, 54.2, 75.6, 65.7, 97.4, 83.9, 65.4, 97.4, 72.7 \][/tex]
2. Identify the number that appears most frequently. Here, 97.4 appears 3 times.
Thus, the mode weight of the artichokes is 97.4 grams.
To summarize:
- Mean: 78.85 grams
- Median: 77.2 grams
- Mode: 97.4 grams
### Mean
To find the mean (average) weight, we add all the weights together and then divide by the number of weights.
List of artichoke weights:
[tex]\[ 78.8, 97.4, 54.2, 75.6, 65.7, 97.4, 83.9, 65.4, 97.4, 72.7 \][/tex]
1. Add all the weights:
[tex]\[ 78.8 + 97.4 + 54.2 + 75.6 + 65.7 + 97.4 + 83.9 + 65.4 + 97.4 + 72.7 = 788.5 \][/tex]
2. Divide by the number of weights (10 in this case):
[tex]\[ \frac{788.5}{10} = 78.85 \][/tex]
So, the mean weight of the artichokes is 78.85 grams.
### Median
To find the median, we need to arrange the weights in order and find the middle value.
1. Arrange the weights in ascending order:
[tex]\[ 54.2, 65.4, 65.7, 72.7, 75.6, 78.8, 83.9, 97.4, 97.4, 97.4 \][/tex]
2. Since there are 10 weights (an even number), the median is the average of the 5th and 6th values:
[tex]\[ \text{5th value: } 75.6, \quad \text{6th value: } 78.8 \][/tex]
3. Calculate the average of these two values:
[tex]\[ \frac{75.6 + 78.8}{2} = 77.2 \][/tex]
So, the median weight of the artichokes is 77.2 grams.
### Mode
The mode is the weight that appears most frequently.
1. Count the frequency of each weight:
[tex]\[ 78.8, 97.4, 54.2, 75.6, 65.7, 97.4, 83.9, 65.4, 97.4, 72.7 \][/tex]
2. Identify the number that appears most frequently. Here, 97.4 appears 3 times.
Thus, the mode weight of the artichokes is 97.4 grams.
To summarize:
- Mean: 78.85 grams
- Median: 77.2 grams
- Mode: 97.4 grams
