Question

Let p be the mean of m observations and q be the mean of n observations, where p ≤ q. If the combined mean of (m + n) observations is c, then which one of the following is correct?
1. c ≤ p
2. c ≥ q
3. p ≤ c ≤ q
4. q ≤ c ≤ p

Answer 1

Correct Answer - Option 3 : p ≤ c ≤ q

Given:

Mean of m observations = p

Mean of n observations = q

Mean of (m + n) observations = c 

Concept:

Mean: The mean is defined as the sum of the observations

divided by the total number of observations. 

Calculation:

According to the question,

⇒ Total sum of m observations = pm

⇒ Total sum of n observations = qn

⇒ Total sum of m and n observations = pm + qn

⇒ c = (pm + qn)/(m + n)

As, p ≤ q,

∴ From above, p ≤ c ≤ q is option is correct.