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The following 13 observations are molecular weights of 13 compounds (in amu): 65, 61, 63, 65, 61, 60, 65, 83, 65, 84, 61, 65, 62 Which of
Question

The following 13 observations are molecular weights of 13 compounds (in amu):
65, 61, 63, 65, 61, 60, 65, 83, 65, 84, 61, 65, 62
Which of the following is true of the molecular weights?

A.

Mean = Median < Mode

B.

Median < Mode = Mean

C.

Mode = Median < Mean

D.

Median = Mean < Mode

Correct option is C


Concept:
Mean = sum of observation/Total number of observation
Median = median is the middle value that separates the higher half from the lower half of the set of observations.
Mode = Mode is most frequently occurring observation.
Solution:
The following 13 observations are molecular weights of 13 compounds (in amu):
65, 61, 63, 65, 61, 60, 65, 83, 65, 84, 61, 65, 62
Clearly, 65 is the most occurring observation.
⇒ Mode = 65    ........ (1)
Now, arrange all observations in ascending order
60, 61, 61, 61, 62, 63, 65, 65, 65, 65, 65, 83, 84
⇒ Median = 65      ......... (2)
By (1) & (2) 
Mode = Median
Hence, Option (c) is true.
Final Answer:
(c) Mode = Median < Mean.

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