Answer to Question #284187 in Statistics and Probability for Hanumna

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:

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