Download Understanding Frequency Distribution: Class Limits, Intervals, and Size and more Study notes Calculus in PDF only on Docsity!
Lecture 3
TECHNICAL OF FORMULETED A FREQUENCY
DISTRIBUTION
Nariman Yayha Othman
Technical terms used in formulation frequency distribution
a) Class limits:
The class limits are the smallest and largest values in the class.
Ex :
0 โ 10, in this class, the lowest value is zero and highest value is 10. the two boundaries of the class are called upper and lower limits of the class. Class limit is also called as class boundaries.
b) Class intervals
The difference between upper and lower limit of class is known as class interval.
Ex :
In the class 0 โ 10, the class interval is (10 โ 0) = 10. The formula to find class interval is gives on below
R
L S
i
L = Largest value S = Smallest value R = the no. of classes
Ex :
If the mark of 60 students in a class varies between 40 and 100 and if we want to form 6 classes, the class interval would be
I= (L-S ) / K = 6
= 10 L = 100
S = 40
K = 6
Therefore, class intervals would be 40 โ 50, 50 โ 60, 60 โ 70, 70 โ 80, 80 โ 90 and 90 โ 100.
๏จ Methods of forming class-interval
a) Exclusive method (overlapping)
In this method, the upper limits of one class-interval are the lower limit of next class. This method makes continuity of data.
Ex :
Marks No. of students
20 โ 30 5
30 โ 40 15
40 โ 50 25
A student whose mark is between 20 to 29.9 will be included in the 20 โ 30 class.
Better way of expressing is Marks No. of students
20 to les than 30 (More than 20 but les than 30)
30 to les than 40 15
40 to les than 50 25
Total Students 50
b) Inclusive method (non-overlaping)
Ex :
Marks No. of students
20 โ 29 5
30 โ 39 15
40 โ 49 25
A student whose mark is 29 is included in 20 โ 29 class interval and a student whose mark in 39 is included in 30 โ 39 class interval.
๏จ Class Frequency
The number of observations falling within class-interval is called its class frequency.
a) The classes should be clearly defined and each observation must belong to one and to only one class interval. Interval classes must be inclusive and non- overlapping. b) The number of classes should be neither too large nor too small. Too small classes result greater interval width with loss of accuracy. Too many class interval result is complexity. c) All intervals should be of the same width. This is preferred for easy computations.
The width of interval = Numberofclasses
Range
d) Open end classes should be avoided since creates difficulty in analysis and interpretation. e) Intervals would be continuous throughout the distribution. This is important for continuous distribution. f) The lower limits of the class intervals should be simple multiples of the interval.
Ex : A simple of 30 cars speed of a particular street are as follows with accuracy of 1 km/hr. Construct a frequency distribution for the given data.
62 58 58 52 48 53 54 63 69 63 57 56 46 48 53 56 57 59 58 53 52 56 57 52 52 53 54 58 61 63
๏จ Steps of construction
Step 1
Find the range of data (H) Highest value = 69
(L) Lowest value = 46 Range = H โ L = 69 โ 46 = 23
Step 2
Find the number of class intervals. Sturges formula K = 1 + 3.322 log N. K = 1 + 3.222 log 30 K = 5.90 Say K = 6 ๏ No. of classes = 6
Step 3
Width of class interval
Width of class interval (W) = Numberofclasses
Range = 3. 883 4 6
๏ฝ ๏ ๏ W=
Step 4
Conclusions the class limits and all frequencies belong to each class interval and assign this total frequency to corresponding class intervals as follows:
For first class the limits will collected as follows:
L.C 1 (lower limit of class) = (L) = 46
U.C 1 (upper limit of class) = L.Ci + width of class (W) โ acc. (accuracy)= 46+4-1= 49
For the rest of the classes(i=>2): L.Ci(lower limit of class) = U.Ci-1 + acc. = 49 +1 = 50
U.Ci(upper limit of class) = L.Ci + width of class (W) โ acc. (accuracy)= 50+4-1 =
Class interval Tally bars Frequency 46 โ 49 | | | 3 50 โ 53 | | | |^ | | |^8 54 โ 57 | | | |^ | | |^8 58 โ 61 | | | |^ |^6 62 โ 65 | | | | 4 66 โ 69 | 1
