# SSC CGL Tier 2 Paper 3 | JSO Study Material & online test series Day 2

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# SSC CGL Tier 2 Paper 3 | JSO Study Material & online test series

SSC CGL Tier 2 Paper 3 | JSO Study Material & online test series

Dear Students,

Here, we are providing study material of Paper 3 [JSO] for SSC CGL tier 2. These  are also covering statistics syllabus For Statistical Investigator Grade-II and Assistant Audit officer (for Junior Statistical Officer (JSO), Ministry of Statistics & Programme Implementation) syllabus for cgl 2018-19.

You can also see the SSC CGL  Maths, Reasoning, G.K. and English Questions with detailed solution on our website. All the candidates who are preparing for SSC CGL 2018 must start their preparation according to the syllabus and exam pattern.

We wish you all good luck for the upcoming SSC Exams.

Graphs and Chart: Frequency Distribution

1. Frequency distribution

A frequency distribution is a table that shows ‘’classes" or ‘’intervals" of data entries with a count of the number of entries in each class. The frequency f of a class is the number of data entries in the class. Each class will have a ‘’lower class limit" and an ‘’upper class limit" which are the lowest and highest numbers in each class. The ‘’class width" is the distance between the lower limits of consecutive classes. The range is the difference between the maximum and minimum data entries.

The class width is the distance between lower (or upper) limits of consecutive classes.

The range is the difference between the maximum and minimum data entries.

Steps for constructing a frequency distribution from a data set

1. If the number of classes is not given, decide on a number of classes to use. This number should be between 5 and 20.
2. Find the class width: Determine the range of the data and divide this by the number of classes. round up to the next convenient number (if it's a whole number, also round up to the next whole number).
3. Find the class limits: You can use the minimum data entry as the lower limit of the first class. To get the lower limit of the next class, add the class width. Continue until you reach the last class. Then find the upper limits of each class (since the classes cannot overlap, and occasionally your data will include decimal numbers, remember that it's ne for the upper limits to be decimals).
4. Count the number of data entries for each class, and record the number in the row of the table for that class. (The book recommends using\tally" marks to count).

Example

Make a frequency distribution for the following data, using 5 classes:

5        10        7      19      25      12      15       7      6      8

17       17       22      21      7        7       24       5      6      5

The smallest number is 5, and the largest is 25, so the range is 20. The class width will be 20/5 = 4, but we need to round up, so we will use 5. Our classes will be 5-9, 10-14, 15-19, 20-24, and 25-29.

Then, counting the number of entries in each class, we get:

Note that the sum of the frequencies is 20, which is the same as number of data entries that we had. You can add more information to your frequency distribution table. The ‘’midpoint’’ (or ‘’class mark") of each class can be calculated as:

Midpoint =              Lower class limit + Upper class limit/2

The ‘’relative frequency’’ of each class is the proportion of the data that falls in that class. It can be calculated for a data set of size n by:

Relative frequency =  Class Frequency/sample size      =   f/n

The ‘’cumulative frequency’’ is the sum of the frequencies of that class and all previous classes.

• Frequency Histogram

A frequency histogram is a graphical way to summarize a frequency distribution. It is a bar graph with the following properties:

1. The horizontal scale is quantitative and measures the data values.
2. The vertical scale measures the frequencies of the classes.
3. Consecutive bars must touch. As a result, the ‘’class boundaries’’ are the numbers that separate classes without forming gaps. They will be the lower limits of classes as calculated for a frequency distribution.
1. Cumulative Frequency Graph

A cumulative frequency graph or ogive is a line graph displaying the cumulative frequency of each class at its upper class boundary. The upper boundaries are marked on the horizontal axis, and the cumulative frequencies are marked on the vertical axis. The graph should start at (or just before) the lower boundary of the first class (where the cumulative frequency is zero), and end at the upper boundary of the last class. The graph should be increasing from left to right, and the points should be evenly spaced along the horizontal axis.

Diagrammatic Presentation of Frequency Distribution

Histogram is the most common form of diagrammatic representation of a grouped frequency distribution. It consists of a set of adjoining rectangles drawn on a horizontal base line. Width of rectangles, one for each class, extends over the class boundaries (not class limits) shown on the horizontal scale.