The mean and standard deviation of the marks of 10 students were found to be 50 and 12 respectively. Later, it was observed that two marks 20 and 25 were wrongly read as 45 and 50 respectively. Then t

Question

The mean and standard deviation of the marks of 10 students were found to be 50 and 12 respectively. Later, it was observed that two marks 20 and 25 were wrongly read as 45 and 50 respectively. Then the correct variance is

Canvas Classes · Accepted Answer

🧠 Two Corrections — Update  and , Then Recompute

The standard "fix-the-mistake" workflow. Two wrong values:  and . Update  and  for both, recompute the mean, then compute variance.

The habit: track  and  as your two stateful quantities. Apply each correction additively.

🗺️ Working It Out

Original: , .

Corrections:  (subtract , add ) and  (subtract , add ).

Correct .

Correct mean .

Correct variance .

⚡ The Smart Move

The change in  for one correction is . Here: . So  drops

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More questions from this chapter