Question

Using Data Below, Compute for the following. Show the Correct and Complete solution

a. Mean

b. Median

c. Mode

d. Standard Deviation

21, 27, 28, 20, 18, 18, 19, 17, 22, 24, 23, 27, 26, 25, 26, 25, 22, 21, 22, 26, 28, 26, 20, 19, 17,18, 26, 27, 27, 22, 23, 25, 25, 27, 28, 20, 19, 17, 16,16, 20,16, 21, 26, 27, 26, 28,16, 25, 28

Answer 1

$16, 16, 16, 16, 17, 17, 17, 18, 18, 18, 19, 19, 19,$

$20, 20, 20, 20, 21, 21, 21, 22, 22, 22, 22, 23, 23,$

$24, 25, 25, 25, 25, 25, 26, 26, 26, 26, 26, 26, 26,$

$27, 27, 27, 27, 27, 27, 28, 28, 28, 28, 28$

a.

$$Mean=\dfrac{1}{50}\big(16(4)+17(3)+18(3)+19(3)$$

$$+20(4)+21(3)+22(4)+23(2)+24+25(5)$$

$$+26(7)+27(6)+28(5)\big)=\dfrac{1136}{50}=22.72$$

b.

$$Median=\dfrac{23+23}{2}=2$$

c.

$$Mode=26, \text{appeared 7 times}$$

d.

$$s^2=\dfrac{\displaystyle\sum_{i=1}^n(x_i-\bar{x})^2}{n-1}$$

$$\displaystyle\sum_{i=1}^{50}(x_i-\bar{x})^2$$

$$=(16-22.72)^2(4)+(17-22.72)^2(3)+(18-22.72)^2(3)$$

$$+(19-22.72)^2(3)+(20-22.72)^2(4)+(21-22.72)^2(3)$$

$$+(22-22.72)^2(4)+(23-22.72)^2(2)+(24-22.72)^2$$

$$+(25-22.72)^2(5)+(26-22.72)^2(7)+(27-22.72)^2(6)$$

$$+(28-22.72)^2(5)=780.08$$

$$s^2=\dfrac{780.08}{50-1}=15.92$$

$$Standard\ deviation=s=\sqrt{s^2}=\sqrt{15.92}=3.99$$