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

1.

a. Median $\tilde{x}=5,$ third value

b. Median $\tilde{x}=16,$ third value

c. Median $\tilde{x}=33.5, \dfrac{31+36}{2}=33.5$

2.

a. $2, 3, 6, 7, 10$

$$Range=10-2=8$$

b. $11, 27, 32, 45, 54$

$$54-11=43$$

3.

$$mean=\bar{x}=\dfrac{1}{6}(13+18+21+19+16+15)$$

$$=17$$

$$Var(X)=\sigma^2 =\dfrac{1}{6}((13-17)^2+(18-17)^2$$

$$+(21-17)^2+(19-17)^2+(16-17)^2$$

$$+(15-17)^2)=7$$

$$\sigma=\sqrt{\sigma^2}=\sqrt{7}\approx2.645751$$