For a statistical data x1,x2,…,x10 of 10 values, a student obtained the mean as 5.5 and ∑i=110xi2=371. He later found that he had noted two values in the data incorrectly as 4 and 5, instead of the correct values 6 and 8, respectively. The variance of the corrected data is
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Step-by-Step Solution
Step 1: Calculate the incorrect sum of observations
The mean of a dataset is calculated by dividing the sum of all observations by the number of observations. We are given the incorrect mean and the number of observations, so we can find the incorrect sum of observations.
Step 2: Calculate the correct sum of observations
To find the correct sum of observations, we subtract the incorrectly noted values from the incorrect sum and add the correct values. The incorrect values were 4 and 5, and the correct values are 6 and 8.
Step 3: Calculate the correct sum of squares
Similarly, to find the correct sum of squares, we subtract the squares of the incorrectly noted values from the incorrect sum of squares and add the squares of the correct values. The incorrect sum of squares was given as 371.
Step 4: Calculate the correct mean
Now that we have the correct sum of observations, we can calculate the correct mean by dividing it by the total number of observations, which is 10.
Step 5: Calculate the variance of the corrected data
The variance is calculated using the formula: sum of squares divided by the number of observations, minus the square of the mean. We use the corrected sum of squares and the corrected mean for this calculation.