Question

Four pieces of wooden sticks P, Q, R and S are placed along the length of 15 cm long scale as shown in the figure. What is the average length of these sticks?

A) 2.0 cm
B) 2.5 cm
C) 2.6 cm
D) 2.9 cm

Answer 1

Hint In this question we are going to find the average length of sticks P, Q, R and S. The total length of scale is given and in the diagram we can see the approximate lengths of these sticks.

Complete step by step solution:
Given,
The length of scale $L = 15{\text{ cm}}$
From figure, we can see that the length of sticks P, Q, R and S are as follows,
P=2.1 cm
Q= 3 cm
R= 3.1 cm
S= 2.5 cm
Now using the formula for average length of sticks,
\[\Rightarrow {\text{Average length of sticks = }}\dfrac{{P + Q + R + S}}{4}\]
Putting the values of P, Q, R and S
\[\Rightarrow {\text{Average length of sticks = }}\dfrac{{2.1 + 3 + 3.1 + 2.5}}{4}\]
\[\Rightarrow {\text{Average length of sticks = }}\dfrac{{10.7}}{4}\]
\[\Rightarrow {\text{Average length of sticks = }}2.675{\text{ cm}}\]
\[\Rightarrow {\text{Average length of sticks = }}2.6{\text{ cm}}\]
Result- the average length of sticks P, Q, R and S is \[2.6{\text{ cm}}\].

Hence, option (C) is correct.

Note: In this question we have to be careful while finding the lengths of sticks P, Q, R and S by taking the reference of the given scale. This is a question of general knowledge of finding average. If there are N number of elements and the elements are ${N_1},{N_2},{N_3}..........$.Then the general formula of average is as follows,
${\text{Average = }}\dfrac{{{\text{sum of all the elements}}}}{{{\text{total number of elements}}}}$
${\text{Average = }}\dfrac{{{{\text{N}}_1} + {{\text{N}}_2} + {{\text{N}}_3} + ........}}{N}$
It is an important topic of qualitative aptitude. A set of elements can be considered as a sequence of numbers. This sequence can have unevenly spaced numbers. The average of numbers present in a set of elements can be considered as the mean of these elements. We can say one more thing about average that average is a single number that we use to present a set of numbers. A very common formula to find average of numbers of set can be written as follows,
${\text{Average = }}\dfrac{{{\text{sum}}}}{{{\text{count}}}}$