Question

Calculate the quartiles, (i,e., Q1 and Q3,), deciles D3 and D7, Percentiles P10, P23 and P92 for the

following data. Also find the Quartile Range and Quartile Deviation.

Marks 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80

No. of Students 8 7 5 12 28 22 8 10

Answer 1

Quartiles:

Firstly find quartile position;

$Q_1=\frac{1}{4}\times100=25th-position$

$Q_2=\frac{1}{2}\times100=50th-position$

$Q_3=\frac{3}{4}\times100=75th-position$

$Quartile=L+\frac{(Q-P)}{F}\times C$

$Q_1=30+\frac{(25-20)}{12}\times 10=34.2$

$Q_2=40+\frac{(50-32)}{28}\times 10=46.4$

$Q_3=50+\frac{(75-60)}{22}\times 10=56.8$

Deciles:

$D_3=l+\frac{w}{f}(\frac{4N}{10}-C)=30.5+\frac{10}{32}(\frac{3\times100}{10}-20)=33.6$

$D_7=l+\frac{w}{f}(\frac{4N}{10}-C)=50.5+\frac{10}{82}(\frac{7\times100}{10}-60)=51.7$

Percentiles:

$P_k=L_k+\frac{\frac{nk}{100}-F_k}{f_k}\times C_w$

P₁₀ $=10.5+\frac{\frac{100\times10}{100}-8}{15}\times 10=11.8$

P₂₃ $=30.5+\frac{\frac{100\times23}{100}-20}{32}\times 10=31.4$

P₉₂ $=70.5+\frac{\frac{100\times92}{100}-90}{100}\times 10=70.7$

Quartile Range:

$QR=Q_3-Q_1=56.8-34.2=22.6$

Quartile Deviation:

$QD=\frac{Q_3-Q_1}{2}=\frac{56.8-32.2}{2}=11.3$