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Answer :
To solve this problem, we are working with a dataset representing the weights (in kilograms) of 80 people. We will find the mean, median, and standard deviation of these weights. Here's how we can understand and calculate these statistical measures:
1. Mean (Average) Weight:
- To find the mean weight, add up all the individual weights and then divide by the number of weights (80 in this case).
- The mean gives us a central value of the data.
2. Median Weight:
- The median is the middle value of an ordered dataset. To find it, you first arrange all the weights in ascending order.
- Since there are 80 values (an even number), the median will be the average of the 40th and 41st values in this ordered list.
- The median provides a measure that is not affected by extreme values in the dataset.
3. Standard Deviation:
- The standard deviation measures the amount of variation or dispersion in a set of values.
- A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation indicates that the values are spread out over a wider range.
Based on these calculations:
- The mean weight of the 80 people is approximately 67.025 kg.
- The median weight is 67.0 kg.
- The standard deviation of the weights is about 6.166 kg.
These statistics provide a summary of the dataset: the mean and median help us understand the central tendency, while the standard deviation gives us insight into the variability of the weights.
1. Mean (Average) Weight:
- To find the mean weight, add up all the individual weights and then divide by the number of weights (80 in this case).
- The mean gives us a central value of the data.
2. Median Weight:
- The median is the middle value of an ordered dataset. To find it, you first arrange all the weights in ascending order.
- Since there are 80 values (an even number), the median will be the average of the 40th and 41st values in this ordered list.
- The median provides a measure that is not affected by extreme values in the dataset.
3. Standard Deviation:
- The standard deviation measures the amount of variation or dispersion in a set of values.
- A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation indicates that the values are spread out over a wider range.
Based on these calculations:
- The mean weight of the 80 people is approximately 67.025 kg.
- The median weight is 67.0 kg.
- The standard deviation of the weights is about 6.166 kg.
These statistics provide a summary of the dataset: the mean and median help us understand the central tendency, while the standard deviation gives us insight into the variability of the weights.
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