Answer to Question #285608 in Statistics and Probability for Jimin

Question

There are the scores of 20 students in a 20-item test in Mathematics in the Modern World: 1, 7, 9, 4, 12, 15, 18, 20, 15, 14, 13, 15, 20, 20, 3, 5, 16, 18, 15 and 13. Find the following:

Answers:

1. Quartile3 =

2. Decile4 =

3. Percentile75 =

Answer 1

$$\def\arraystretch{1.5} \begin{array}{c:c:c} x_i & f_i & cf \\ \hline 1 & 1 & 1 \\ \hdashline 3 & 1 & 2 \\ \hdashline 4 & 1 & 3 \\ \hdashline 5 & 1 & 4 \\ \hdashline 7 & 1 & 5 \\ \hdashline 9 & 1 & 6 \\ \hdashline 12 & 1 & 7 \\ \hdashline 13 & 2 & 9 \\ \hdashline 14 & 1 & 10 \\ \hdashline 15 & 4 & 14 \\ \hdashline 16 & 1 & 15 \\ \hdashline 18 & 2 & 17 \\ \hdashline 20 & 3 & 20 \\ \hdashline & n=20 & \\ \end{array}$$

1.

$Q_3=(\dfrac{3(n+1) }{4})^{th}$ value of the observation

$=(\dfrac{3(20+1) }{4})^{th}$ value of the observation

$=(15.75)^{th}$ value of the observation

$Q_3=18$

2.

$D_4=(\dfrac{4(n+1) }{10})^{th}$ value of the observation

$=(\dfrac{4(20+1) }{10})^{th}$ value of the observation

$=(8.4)^{th}$ value of the observation

$D_4=13$

3.

$P_{75}=(\dfrac{75(n+1) }{100})^{th}$ value of the observation

$=(\dfrac{75(20+1) }{100})^{th}$ value of the observation

$=(15.75)^{th}$ value of the observation

$P_{75}=18$