Question

7. The result of test in a math class is summarized in a frequency distribution table below. (a) (6 points) Complete the frequency distribution table below: Letter Class Class Class Cumulative Percentage Grade Limits Midpoint Frequency Frequency Frequency D 58-68 10 с 69-79 12 B 80-90 24 A 91-101 4 (b) (4 points) Find Sof the frequency distribution table in reduced fraction by using class midpoints and class frequecies. (b) (c) (5 points) Draw its pie chart graph using letter grades and percentage fre- quency. Clearly label and mark your graph.

Answer 1

(a)

The class midpoint is the lower class limit plus the upper-class limit divided by 2.

Cumulative frequency is calculated by adding the previous frequencies.

Percentage Frequency is calculated by (class freq. x 100) / (Sum of all frequency)

A B C D E F G H Class Letter Grade Class Limits Cumulative Frequency Percentage Frequency Frequency Class Midpoint =C3+(C3-B3)/2 73 2 =F3/SUM($E$3:$E$6)*100 20 3 D 58 69 68 79 10 12 4 C 84 44 10 = 10 22 = (12+10) 46 24+22 50 = 4+46 5 B 80 95 92 90 101 24 4 6 A 91 106 100

(b) to find S² we have to first find the mean.

The mean ($\mu$) is the sum of f⋅M divided by n, which is the sum of frequencies.

μ = Σf - M ΣΗ

A B с D F Class Midpoint E Class Frequency f Letter Grade Class Limits f.M м 1 2 3 D 4. C 58 68 10 69 79 =C3+(C3-B3)/2 73 84 95 106 12 24 =E3*D3 730 1008 2280 424 4442 80 5 B 6 A 90 101 91 4 7 50 8 q

$\mu = \frac{4442}{50}=88.84$

The formula for standard deviation is:

Σ1 - Μ? – η(μ)? s2 η –1

A B C D E G F Class Frequency Letter Grade Class Midpoint M Class Limits M? f.M? 1 f 2 3 D 4 C 5 B 6 A 58 69 68 79 =C3+(C3-B3)/2 =POWER(D3,2) 73 5329 84 7056 95 9025 106 11236 10 12 =F3*E3 53290 84672 216600 44944 399506 90 24 80 91 101 4 50 7 C

$S^2 = \frac{399506-50(88.84)^2}{50-1}=\frac{17424}{175}$

(c)

Angles for each sector are calculated using: (% freq. x 360/100 = (20*360)/100

Letter Grade	Class Frequency f	Percentage Frequency	Angle
D	10	20	72
C	12	24	86.4
B	24	48	172.8
A	4	8	28.8
	50

PIE Chart 8% D 20% D ПС B B 48% с 24% A

If it helps, kindly upvote.

Comment below for doubt