Question

5
For a continuous data distribution, 10-20 with frequency 3, 20-30 with frequency 5, 30 40 with frequency
7and 40-50 with frequency 1, the value of quartile deviation is.
Select one:
O a. 2
O b. 6.85
O c. 6:32
d. 10​

Answer 1

Answer:

Quartile deviation=6.85

Explanation:

Tabulating the data:

             $\left\begin{array}{cccc}S.No&Classinterval&frequency&cumulativefrequency\\1&10-20&3&3\\2&20-30&5&3+5=8\\3&30-40&7&8+7=15\\4&40-50&1&15+1=16\end{array}\right$

Here, $N=16$

To find the interval of $Q_{1}$, $i\frac{N}{4} = 1\frac{16}{4}=4$

So, $Q_{1}$ lies in the interval 20-30

And for $Q_{3},$ $i\frac{N}{4} = 3\frac{16}{4}=12$

So, $Q_{3}$ lies in the interval 30-40

Formula for Quartile is $Q_{n} =l_{1} +\frac{i(\frac{N}{4} )-c}{f} (l_{2}-l_{1} )$

Substituting the values for $Q_{1}$,

                                              $Q_{1} =20+\frac{4-3}{5} (30-20)\\\\ =20+\frac{1}{5} (10)=22$  

Substituting the values for $Q_{3}$,

                                              $Q_{3} =30+\frac{12-8}{7} (40-30)\\\\ =30+\frac{4}{7} (10)=35.71$

Quartile deviation, $Q.D=\frac{Q_{3}- Q_{1}}{2}$

                                       $=\frac{35.71-22}{2} =6.85$

So, the correct answer is option b.