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Mean, Median and Mode · Question 50 of 67

Question 50

HardOriginal question

The mean of 10 observations is 50. Each of the first 4 observations is increased by 5 and each of the other 6 is decreased by 4. What is the new mean?

Options for question 50

Show the answer and explanation
CorrectNot quiteAnswer A

Correct answer: A

Explanation

  1. Change in total = 4×5−6×4=20−24=−44 \times 5 - 6 \times 4 = 20 - 24 = -4.

  2. Change in mean = −410=−0.4\frac{-4}{10} = -0.4.

  3. New mean = 50−0.4=49.650 - 0.4 = 49.6.

Worth noting

50.5 averages the two changes (+5 and −4) as if both groups had the same size. 51 adds 5 and subtracts 4 once each. The groups are 4 and 6 in size, so weigh each change by its group.

Concept
Mean when different groups change by different amounts
Typical time
120 s
Your time
—
The rule this testsWhen values change
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