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Answer :
Sure! Let's go through the solution step by step to find the mean, median, mode, range, and interquartile range (IQR) for the given data set of weights: 217, 212, 285, 245, 301 pounds.
### a) Mean:
The mean is calculated by adding up all the numbers in the data set and then dividing by the number of values.
1. Add the weights together: 217 + 212 + 285 + 245 + 301 = 1260
2. Divide by the number of weights (which is 5): 1260 ÷ 5 = 252
So, the mean weight is 252.0 pounds.
### b) Median:
The median is the middle number in a sorted, ascending or descending list of numbers.
1. First, sort the weights: 212, 217, 245, 285, 301
2. Since there are 5 weights, the middle one is the third value.
So, the median weight is 245.0 pounds.
### c) Mode:
The mode is the number that appears most frequently in a data set. If no number repeats, there is no mode.
- In this set: 212, 217, 245, 285, 301, each number appears only once, so there is technically no mode.
Thus, there is no mode in this data set.
### d) Range:
The range is the difference between the highest and lowest values.
1. Highest weight is 301 and lowest is 212.
2. Subtract the lowest from the highest: 301 - 212 = 89
Therefore, the range of weights is 89 pounds.
### e) Interquartile Range (IQR):
The IQR measures the spread of the middle 50% of the data and is calculated as the difference between the third quartile (Q3) and the first quartile (Q1).
1. First quartile (Q1) is the median of the first half: 212, 217, 245
- Median of 212, 217 is 214.5
2. Third quartile (Q3) is the median of the second half: 245, 285, 301
- Median of 285, 301 is 293.0
Calculate IQR: Q3 - Q1 = 293.0 - 214.5 = 68.5
Thus, the interquartile range (IQR) is 68.0 pounds.
That concludes the step-by-step process for finding the mean, median, mode, range, and IQR for the set of weights.
### a) Mean:
The mean is calculated by adding up all the numbers in the data set and then dividing by the number of values.
1. Add the weights together: 217 + 212 + 285 + 245 + 301 = 1260
2. Divide by the number of weights (which is 5): 1260 ÷ 5 = 252
So, the mean weight is 252.0 pounds.
### b) Median:
The median is the middle number in a sorted, ascending or descending list of numbers.
1. First, sort the weights: 212, 217, 245, 285, 301
2. Since there are 5 weights, the middle one is the third value.
So, the median weight is 245.0 pounds.
### c) Mode:
The mode is the number that appears most frequently in a data set. If no number repeats, there is no mode.
- In this set: 212, 217, 245, 285, 301, each number appears only once, so there is technically no mode.
Thus, there is no mode in this data set.
### d) Range:
The range is the difference between the highest and lowest values.
1. Highest weight is 301 and lowest is 212.
2. Subtract the lowest from the highest: 301 - 212 = 89
Therefore, the range of weights is 89 pounds.
### e) Interquartile Range (IQR):
The IQR measures the spread of the middle 50% of the data and is calculated as the difference between the third quartile (Q3) and the first quartile (Q1).
1. First quartile (Q1) is the median of the first half: 212, 217, 245
- Median of 212, 217 is 214.5
2. Third quartile (Q3) is the median of the second half: 245, 285, 301
- Median of 285, 301 is 293.0
Calculate IQR: Q3 - Q1 = 293.0 - 214.5 = 68.5
Thus, the interquartile range (IQR) is 68.0 pounds.
That concludes the step-by-step process for finding the mean, median, mode, range, and IQR for the set of weights.
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