Answer:
70% of the data points
Explanation:
To calculate the percentage of data points that fall within one standard deviation of the mean, you can follow these steps:
Calculate the mean of the data set: (55+54+66+38+53+56+57+66+45+65)/10 = 55
Calculate the standard deviation of the data set: √ (((55-55) ²+(54-55) ²+(66-55) ²+(38-55) ²+(53-55) ²+(56-55) ²+(57-55) ²+(66-55) ²+(65-55)²)/9) = 7.8
Determine the range for data points within one standard deviation of the mean: Mean ± 1 * standard deviation = 55 ± 1 * 7.8 = [47.2, 62.8]
Count the number of data points that fall within this range: 55, 54, 53, 56, 57, 45, and 65 fall within this range.
Calculate the percentage of data points that fall within this range: (7/10) * 100 = 70%
Therefore, 70% of the data points in the given data set fall within one standard deviation of the mean.