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The distributions X and Y with total number of observations 36 and 64, and mean 4 and 3 respectively are combined. What is the mean of the resulting distribution X + Y?
1. 3.26
2. 3.32
3. 3.36
4. 3.42

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Correct Answer - Option 3 : 3.36

Concept:

Mean = \(\rm \dfrac {\text {sum of observations}}{\text {total number of observations}}\)

 

Calculations:

Given, The distributions X and Y with the total number of observations 36 and 64, and mean 4 and 3 respectively are combined.

\(\rm 4 = \dfrac {X}{36}\) and \(\rm 3 = \dfrac {Y}{64}\)

⇒ X = 144 and Y = 192

⇒ X + Y = 144 + 192

⇒ X + Y = 336

Total number of observations =  36 + 64 = 100

Mean = \(\rm \dfrac {\text {sum of observations}}{\text {total number of observations}}\)

⇒ Mean = \(\dfrac {336}{100}\)

⇒ Mean = 3.36

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