Question 1201185
i think it's going to work like this.
the mean of 4500 * 20 = sum of 90,000
subtract 13000 from that and add 3000 to that leaves a sum of 80000.
divide that by 20 to get a new mean of 4000.
square the original standard deviation of 2540 to get a variance of 64516001.
mutliply that by 20 to get a sum of squares of 129032000.
13000 - 4500 = original deviation of 8500.
square that to get a squared deviation of 72250000.
subtract that from the original sum of squares to get a sum of squares of 56782000.
3000 - 4000 = revised deviation of -1000.
square that to get a squared deviation of 1000000.
add that to the sum of squares to get a revised sum of squares of 57782000.
divide that by 20 to get a new variance of 2889100.
take the square root of that to get a new standard deviation of 1699.735274.
if i did this correctly, your solution should be:
mean of corrected claims is 4000.
standard deviation of corrected claims is 1699.735274.
here's a reference on how to calculate standard deviation.
<a href = "https://www.mathsisfun.com/data/standard-deviation-formulas.html" target = "_blank">https://www.mathsisfun.com/data/standard-deviation-formulas.html</a>