Answer to Question #338681 in Statistics and Probability for shimmy

Question

The weights of the students in a class are the following: 69, 70, 75, 66, 83, 88, 66, 63, 61, 68, 73, 57, 52, 58, and 57.

8. Find the value of D8 of the students’ weights.

9. Calculate the value of D4 of the students’ weights.

10. What is the Q2 of the students’ weights?

Answer 1

Arranging Observations in the ascending order, we get :

$$52,57,57,58,61,63,66,66,68,69, 70, 73,75, 83, 88$$

8.

$n=15$

$$D_8=(\dfrac{8(n+1)}{10})^{th} \text{value of the observation}$$

$$=(\dfrac{8(15+1)}{10})^{th} \text{value of the observation}$$

$$=(12.8)^{th} \text{value of the observation}$$

$$=(12)^{th} \text{observation}+0.8((13)^{th}-(12)^{th})$$

$$=73+0.8(75-73)=74.6$$

9.

$n=15$

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

$$=(\dfrac{4(15+1)}{10})^{th} \text{value of the observation}$$

$$=(6.4)^{th} \text{value of the observation}$$

$$=(6)^{th} \text{observation}+0.4((7)^{th}-(6)^{th})$$

$$=63+0.4(66-63)=64.2$$

10.

$n=15$

$$Q_2=(\dfrac{2(n+1)}{4})^{th} \text{value of the observation}$$

$$=(\dfrac{2(15+1)}{4})^{th} \text{value of the observation}$$

$$=(8)^{th} \text{value of the observation}$$

$$=66$$