Answer to Question #156407 in Math for its me gel

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.

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

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

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

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

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

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

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

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

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