Frequency Distribution

2 Pages 391 Words

FREQUENCY DISTRIBUTION

I. Identify the problem

A randomly selected group of students in a class of 35 was asked how much allowance is given to them on a per day basis. The objective is to assess how much the average student gets on a daily basis, find how many of these students fall within a specified class interval using a frequency table, and how much the majority of the students get per day.

II. Data:


100 200 300 500 100
200 250 450 300 700
250 350 200 250 100
500 200 150 150 150
150 150 300 350 250
250 300 350 250 250
400 350 400 300 400




Allowances per day of a group of 35 students studying at DLSU
(in Php)

III. Set-up the frequency table


Class interval:
=1 + 3.322log35
=6.12 » 6

Class size:
=(700 – 100)/6
=100

Frequency Table

Class Limits Class Mark Class Frequency Cum. Frequency
100-199 149.5 8 8
200-299 249.5 11 19
300-399 349.5 9 28
400-499 449.5 4 32
500-699 549.5 2 34
700-799 749.5 1 35


IV. Computations for descriptive statistics

Mean:

=(8)(149.5) + (11)(249.5) + (9)(349.5) + (4)(449.5) + (2)(549.5) + (1)(749.5)
35
=Php 306.63

Median:

Median class is 200-299
=200 + 100{ [ (35/2) – 8 ] / 11 }
=Php 286.36

Mode:
Php 250.00

Measures of Variability:

a. Average Deviation

= (8)|49.5-306.63|
+ (11)|249.5-306.63|
(9)|349.5-306.63|
(4)|449.5-306.63|
+ (2)|549.5-306.63|
(1)|749.5-306.63|
3771.39

= 3771.39/35
=Php 107.54

b. Variance/Standard Deviation

Class Limits Class Mark Class Frequency fixi2 fixi
100-199 149.5 8 178,802 1,196
200-299 249.5 11 684,752.75 2,744.5
300-399 349.5 9 1,099,352.25 3,145.5
400-499 449.5 4 808,201 1,798
500-699 549.5 2 603,900.5 1,099
700-799 749.5 1 561,750.25 749.5


nå fixi2 = 35(3,936,758.75)
= 137,786,556.25
(åfixi)2 = (10,732.50)2 = 115,186,556.25

s2 = 137,786,556.25 - 115,186,55...