what can a cumulative relative frequency graph be used to describe
In Statistics, a cumulative frequency is defined as the full of frequencies, that are distributed over dissimilar course intervals. It means that the data and the total are represented in the form of a tabular array in which the frequencies are distributed according to the class interval. In this article, we are going to talk over in item nearly the cumulative frequency distribution, types of cumulative frequencies, and the construction of the cumulative frequency distribution table with examples in detail.
What is Meant by Cumulative Frequency Distribution?
The cumulative frequency is the total of frequencies, in which the frequency of the first grade interval is added to frequency of the second form interval and and so the sum is added to the frequency of the third class interval and so on. Hence, the table that represents the cumulative frequencies that are divided over unlike classes is called the cumulative frequency table or cumulative frequency distribution. More often than not, the cumulative frequency distribution is used to identify the number of observations that lies higher up or below the particular frequency in the provided data set.
Types of Cumulative frequency Distribution
The cumulative frequency distribution is classified into two unlike types namely: less than ogive or cumulative frequency and more/greater than cumulative frequency.
Less Than Cumulative Frequency:
The Less than cumulative frequency distribution is obtained by adding successively the frequencies of all the previous classes along with the class against which information technology is written. In this blazon, the cumulate begins from the everyman to the highest size.
Greater Than Cumulative Frequency:
The greater than cumulative frequency is also known as the more than type cumulative frequency. Hither, the greater than cumulative frequency distribution is obtained by determining the cumulative full frequencies starting from the highest class to the lowest class.
Graphical Representation of Less Than and More than Than Cumulative Frequency
Representation of cumulative frequency graphically is easy and convenient as compared to representing it using table, bar-graph, frequency polygon etc.
The cumulative frequency graph tin be plotted in two ways:
- Cumulative frequency distribution curve(or ogive) of less than type
- Cumulative frequency distribution curve(or ogive) of more than blazon
Steps to Construct Less than Cumulative Frequency Curve
The steps to construct the less than cumulative frequency curve are as follows:
- Mark the upper limit on the horizontal centrality or 10-axis.
- Marker the cumulative frequency on the vertical centrality or y-axis.
- Plot the points (ten, y) in the coordinate plane where ten represents the upper limit value and y represents the cumulative frequency.
- Finally, join the points and draw the smooth curve.
- The curve so obtained gives a cumulative frequency distribution graph of less than blazon.
To draw a cumulative frequency distribution graph of less than type, consider the post-obit cumulative frequency distribution table which gives the number of participants in whatsoever level of essay writing competition according to their age:
Table 1 Cumulative Frequency distribution tabular array of less than type
| Level of Essay | Age Group (class interval) | Age group | Number of participants (Frequency) | Cumulative Frequency |
| Level 1 | 10-15 | Less than 15 | 20 | xx |
| Level two | 15-20 | Less than twenty | 32 | 52 |
| Level 3 | xx-25 | Less than 25 | 18 | 70 |
| Level 4 | 25-30 | Less than 30 | thirty | 100 |
On plotting corresponding points according to table 1, we have
Steps to Construct Greater than Cumulative Frequency Curve
The steps to construct the more than/greater than cumulative frequency curve are as follows:
- Marking the lower limit on the horizontal centrality.
- Mark the cumulative frequency on the vertical centrality.
- Plot the points (10, y) in the coordinate plane where x represents the lower limit value and y represents the cumulative frequency.
- Finally, draw the smooth curve by joining the points.
- The bend and then obtained gives the cumulative frequency distribution graph of more than than type.
To depict a cumulative frequency distribution graph of more than type, consider the aforementioned cumulative frequency distribution table, which gives the number of participants in whatsoever level of essay writing competition co-ordinate to their age:
Tabular array ii Cumulative Frequency distribution table of more than than type
| Level of Essay | Age Group (grade interval) | Age grouping | Number of participants (Frequency) | Cumulative Frequency |
| Level 1 | 10-30 | More than 10 | xx | 100 |
| Level two | 15-thirty | More than 15 | 32 | lxxx |
| Level iii | 20-30 | More than 20 | xviii | 48 |
| Level iv | 25-30 | More than than 25 | thirty | xxx |
On plotting these points, we go a bend every bit shown in the graph 2.
These graphs are helpful in figuring out the median of a given data fix. The median tin can be found out by drawing both types of cumulative frequency distribution curves on the aforementioned graph. The value of of the signal of intersection of both the curves gives the median of the given set of data. For the given table 1, the median can be calculated as shown:
Instance on Cumulative Frequency
Case:
Create a cumulative frequency table for the following information, which represent the number of hours per week that Arjun plays indoor games:
Arjun's game time:
| Days | No. of Hours |
| Monday | 2 hrs |
| Tuesday | 1 hour |
| Wednesday | ii hrs |
| Thursday | three hrs |
| Friday | 4 hrs |
| Sat | 2 hrs |
| Lord's day | 6 hrs |
Solution:
Permit the no. of hours be the frequency.
Hence, the cumulative frequency tabular array is calculated equally follows:
| Days | No. of Hours (Frequency) | Cumulative Frequency |
| Monday | ii hrs | ii |
| Tuesday | 1 hr | two+1 = three |
| Wednesday | 2 hrs | iii+2 = five |
| Th | three hrs | five+iii = 8 |
| Fri | iv hrs | 8+4 = 12 |
| Saturday | ii hrs | 12+2 = fourteen |
| Sunday | 6 hrs | 14+6 = 20 |
Therefore, Arjun spends twenty hours in a calendar week to play indoor games.
Thus using statistics we tin can tackle many existent-life issues. To know more almost statistics, download BYJU'South-The Learning App from Google Play Store.
Oftentimes Asked Questions on Cumulative Frequency Distribution
What is meant by cumulative frequency?
The cumulative frequency (c.f) is defined as the total of frequencies, where the frequency of the first class interval is added to the frequency of the 2d class interval and then the sum is added to the frequency of the tertiary class interval and and so on.
What is meant past cumulative frequency distribution?
A table that shows the cumulative frequencies, which are distributed over different classes is known as the cumulative frequency tabular array or cumulative frequency distribution.
What are the 2 types of cumulative frequencies?
The ii types of cumulative frequencies are less than cumulative frequency and more cumulative frequency.
What is meant by cumulative frequency series?
The series of frequencies that are added continuously corresponding to each class interval is known as the cumulative frequency serial.
How to calculate the cumulative frequency?
The cumulative frequency tin be calculated past adding the frequency of the first form interval to the frequency of the second class interval. After that, the sum is added to the frequency of the third class interval, etc.
Source: https://byjus.com/maths/cumulative-frequency-distribution/
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