For a statistical data of 10 values, a student obtained the mean as 5.5 and . 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 ,

Question

For a statistical data  of 10 values, a student obtained the mean as 5.5 and . 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

Canvas Classes · Accepted Answer

🧠 Two Wrong Values, Two Corrections — Same Workflow as One

Two observations are wrong. The fix is the same as for one wrong value, just applied twice. Update  and  with both corrections, recompute mean and variance.

The habit: for "value(s) replaced" problems, the corrections add up linearly:  changes by  and  changes by .

🗺️ Working It Out

Original . Original .

Two corrections:  and . So  changes by  and  changes by .

Correct . Correct .

Correct mean . Correct variance .

⚡ The Smart M

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