Question

A. Solve the following problems:

1. On the assumption that variables are continuous, compute for the median of the following data:

a. 1, 4, 5, 9, 11

b. 4, 8, 16, 27, 52

c. 7, 26, 31, 36, 46, 65

2. Calculate the range for the following sets of measurements:

a. 3, 6, 7, 10, 2

b. 11, 27, 32, 45, 54

3. Calculate the variance and standard deviation of the following: 13, 18, 21, 19, 16, 15.

Answer 1

Solution:

1.

a.

$$median=5$$

b.

$$median=16$$

c.

$$median=\dfrac{31+36}{2}=33.5$$

2.

a.

$$Range=10-2=8$$

b.

$$Range=54-11=43$$

3.

$$mean=E(X)=\dfrac{1}{6}(13+18+21+19+16+15)$$ $$=\dfrac{102}{6}=17$$ $$Var(X)=\sigma^2=\dfrac{1}{6}((13-17)^2+(18-17)^2$$ $$+(21-17)^2+(19-17)^2+(16-17)^2$$ $$+(15-17)^2)=\dfrac{42}{6}=7$$ $$\sigma=\sqrt{\sigma^2}=\sqrt{7}$$