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