Question

The average of the price per kg. of rice at 10 different places was Rs. 4.85. After a week, the price per kg. was increased by 20 paise at 3 places and decreased by 10 paise at 1 place. The new average of price per kg. is:
(a) Rs. 4.88
(b) Rs. 4.86
(c) Rs. 4.90
(d) Rs. 5.35

Answer 1

Hint: The average of a set of n observations is given by the formula:
 $\text{Average (A)}=\dfrac{\text{Sum of Observations (S)}}{\text{No. of Observations (N)}}$
The average of a set of observations remains unchanged if observations with the same average as the set are added to or removed from the set.
If observations with a different average than the set are added to or removed from the set, then the average of the set changes: $A_{(New)}=A_{(Old)}\pm \dfrac{\text{Change in the Sum}}{\text{Final No. of Observations}}$ .

Complete step-by-step answer:
Let us calculate the total change in the values of prices after one week.
Change = + (3 × 20 paise) - (1 × 10 paise) = + 60 paise - 10 paise = + 50 paise = + 0.5 Rs.
Since, the number of places (number of observations) does not change, Final No. of Observations = 10.
Using the formula $A_{(New)}=A_{(Old)}\pm \dfrac{\text{Change in the Sum}}{\text{Final No. of Observations}}$ , we get:
 $A_{(New)}=4.85+\dfrac{0.5}{10}=4.85+0.05=4.90\text{ Rs./kg}$ .
The correct answer option is (c) Rs. 4.90.

Note: The question can also be solved by finding the sum of the prices of all the 10 places, but it will take a few extra steps.
Using $\text{Average (A)}=\dfrac{\text{Sum of Observations (S)}}{\text{No. of Observations (N)}}$ , we get the sum of the 10 values as:
Sum = Average × Number of Observations
⇒ Sum = 4.85 × 10 = 48.5 Rs.
Final sum after the changes = 48.5 + 0.20 × 3 - 0.10 = 48.4 + 0.60 = 49 Rs.
Final average = $\dfrac{49}{10}=4.9\text{ Rs./kg}$ .
Average is also called Mean.
There are many types of averages: Arithmetic Mean (same sum), Geometric Mean (same product) and Harmonic Mean (same sum of inverses). Usually, average means Arithmetic Mean.