What is the outlier of this set at a 90% confidence level?
42.7 42.8 43.1 43.3 43.5 43.8
To determine the outlier of a set at a 90% confidence level, we need to calculate the range of the set and then identify whether any data point falls outside of that range.
Here are the steps to calculate the outlier and the range:
1. Sort the data set in ascending order:
42.7, 42.8, 43.1, 43.3, 43.5, 43.8
2. Calculate the range of the data set by subtracting the minimum value from the maximum value:
Range = Maximum value - Minimum value = 43.8 - 42.7 = 1.1
3. Determine the boundary values for the outlier at a 90% confidence level:
To identify outliers, we need to consider the boundaries within which 90% of the data points are expected to fall. We can calculate these boundaries by finding the z-scores corresponding to the desired confidence level and applying them to the mean of the data set.
The z-score corresponding to a 90% confidence level is 1.645.
To calculate the boundary values, we find the mean of the data set and add or subtract the product of the z-score and the standard deviation.
Let's assume the data set is normally distributed.
Mean = Sum of all values / Number of values = (42.7 + 42.8 + 43.1 + 43.3 + 43.5 + 43.8) / 6 = 255.2 / 6 = 42.533333
Standard Deviation (σ) = sqrt( [(x1 - mean)^2 + (x2 - mean)^2 + ... + (xn - mean)^2] / n )
= sqrt( [ (42.7 - 42.533333)^2 + (42.8 - 42.533333)^2 + (43.1 - 42.533333)^2 + (43.3 - 42.533333)^2 + (43.5 - 42.533333)^2 + (43.8 - 42.533333)^2 ] / 6 )
After calculating the standard deviation, we can determine the boundary values:
Lower Boundary = Mean - (z-score * standard deviation)
= 42.533333 - (1.645 * standard deviation)
Upper Boundary = Mean + (z-score * standard deviation)
= 42.533333 + (1.645 * standard deviation)
4. Identify any data points that fall outside of the calculated boundary values:
In this case, compare each data point to the lower and upper boundaries. If any data point is less than the lower boundary or greater than the upper boundary, it will be considered an outlier.
From the given data set, we find that there are no data points that fall outside the calculated boundary values. Therefore, there is no outlier in this set at a 90% confidence level.
Remember, the specific steps may differ depending on the approach or assumptions you take in calculating the outlier.