A scientist calculated the mean and standard deviation of a data set to be and . She then found that she was missing one data value from the set. She knows that the missing data value was exactly 3 standard deviations away from the mean. What was the missing data value?
129
147
360
369
To find the missing data value, we need to use the formula for standard deviation, which is:
Standard Deviation = (Data Value - Mean) / Standard Deviation
Given that the missing data value is exactly 3 standard deviations away from the mean, we can substitute the values into the formula:
3 = (Missing Data Value - Mean) / Standard Deviation
Next, we rearrange the formula to solve for the missing data value:
Missing Data Value - Mean = 3 * Standard Deviation
Missing Data Value = Mean + 3 * Standard Deviation
Now, let's plug in the values from the problem:
Missing Data Value = 129 + 3 * 147
Missing Data Value = 129 + 441
Missing Data Value = 570
Therefore, the missing data value is 570.