To find the measure of variability of the dataset, we can calculate the standard deviation.
First, let's find the mean (average) of the dataset:
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Calculate the sum of the data points: \( 9 + 25 + 14 + 16 + 22 + 19 + 22 + 13 + 14 + 14 = 9 + 25 = 34 \) \( 34 + 14 = 48 \) \( 48 + 16 = 64 \) \( 64 + 22 = 86 \) \( 86 + 19 = 105 \) \( 105 + 22 = 127 \) \( 127 + 13 = 140 \) \( 140 + 14 = 154 \) \( 154 + 14 = 168 \)
The sum is \( 168 \).
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Calculate the mean: \[ \text{Mean} = \frac{\text{Sum of data points}}{\text{Number of data points}} = \frac{168}{10} = 16.8 \]
Next, we calculate each data point's deviation from the mean and then square those deviations:
- \( (9 - 16.8)^2 = (-7.8)^2 = 60.84 \)
- \( (25 - 16.8)^2 = (8.2)^2 = 67.24 \)
- \( (14 - 16.8)^2 = (-2.8)^2 = 7.84 \)
- \( (16 - 16.8)^2 = (-0.8)^2 = 0.64 \)
- \( (22 - 16.8)^2 = (5.2)^2 = 27.04 \)
- \( (19 - 16.8)^2 = (2.2)^2 = 4.84 \)
- \( (22 - 16.8)^2 = (5.2)^2 = 27.04 \)
- \( (13 - 16.8)^2 = (-3.8)^2 = 14.44 \)
- \( (14 - 16.8)^2 = (-2.8)^2 = 7.84 \)
- \( (14 - 16.8)^2 = (-2.8)^2 = 7.84 \)
Now, let's sum these squared deviations: \[ 60.84 + 67.24 + 7.84 + 0.64 + 27.04 + 4.84 + 27.04 + 14.44 + 7.84 + 7.84 = 300.6 \]
Now, we find the variance: \[ \text{Variance} = \frac{\text{Sum of squared deviations}}{\text{Number of data points}} = \frac{300.6}{10} = 30.06 \]
Finally, we take the square root to find the standard deviation: \[ \text{Standard Deviation} = \sqrt{30.06} \approx 5.48 \]
However, we don't see a match with the given responses. It seems like we are supposed to find a measure of variability that aligns with one of the options listed (likely the range).
The range is: \[ \text{Range} = \text{Max} - \text{Min} = 25 - 9 = 16 \]
So the best answer based on the options provided is 16.