# SSC CGL Statistics / SSC CGL Tier 2 / SSC CGL Paper 3 JSO

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# SSC CGL Statistics / SSC CGL Tier 2 / SSC CGL Paper 3 JSO

SSC CGL Statistics / SSC CGL Tier 2 / SSC CGL Paper 3 JSO

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.

__Partial values Quartiles, Deciles, Percentiles__

__Introduction__

All of us are aware of the median, which is the middle value or the mean of the two middle values, of an array. We have learned that the median divides a set of data into two equal parts. In the same way, there are also certain other values which divide a set of data into four, ten or hundred equal parts. Such values are referred as quartiles, deciles and percentiles respectively. Collectively, the quartiles, deciles and percentiles and other values obtained by equal sub-division of the data are called Quartiles.

__Quartiles:__

The values which divide an array (a set of data arranged in ascending or descending order) into four equal parts are called quartiles. The first, second and third quartiles are denoted byQ_{1}, Q_{2} and Q_{3} respectively. The first and third quartiles are also called the lower and upper quartiles respectively. The second quartile represents the median, the middle value.

__Quartiles for Ungrouped Data:__

Quartiles for ungrouped data are calculated by the following formulae.

__For Example:__

Following is the data is of marks obtained by 20 students in a test of statistics;

53 74 82 42 39 20 81 68 58 28

67 54 93 70 30 55 36 37 29 61

In order to apply formulae we need to arrange the above data into ascending order i.e. in the form of an array.

20 28 29 30 36 37 39 42 53 54

55 58 61 67 68 70 74 81 82 93

Here, n = 20

The value of 5th item is 36 and that of the 6th item is 37. Thus the first quartile is a value 0.25th of the way between 36 and 37, which are 36.25. Therefore, = 36.25. Similarly,

The value of the 15th item is 68 and that of the 16th item is 70. Thus the third quartile is a value 0.75th of the way between 68 and 70. As the difference between 68 and 70 is 2, so the third quartile will be 68 + 2(0.75) = 69.5. Therefore, Q_{3} = 69.5.

__Quartiles for Grouped Data:__

The quartiles may be determined from grouped data in the same way as the median except that in place of n/2 we will use n/4. For calculating quartiles from grouped data we will form cumulative frequency column. Quartiles for grouped data will be calculated from the following formulae;

Q_{2 }= Median.

Where,

l = lower class boundary of the class containing the Q_{1 }or Q_{3 }i.e. the class corresponding to the cumulative frequency in which n/4 or 3n/4 lies

h = class interval size of the class containing Q_{1 }or Q_{3}

f = frequency of the class containing Q_{1 }or Q_{3}

n = number of values, or the total frequency.

C.F = cumulative frequency of the class preceding the class containing Q_{1 }or Q_{3}

__Deciles__:

The values which divide an array into ten equal parts are called deciles. The first, second,…… ninth deciles D_{1},D_{2}.......D_{9} respectively. The fifth decile D_{5} corresponds to median. The second, fourth, sixth and eighth deciles which collectively divide the data into five equal parts are called quintiles.

**Deciles for Ungrouped Data:**

Deciles for ungrouped data will be calculated from the following formulae;

__Decile for Grouped Data__

Decile for grouped data can be calculated from the following formulae;

Where,

l = lower class boundary of the class containing D_{2} or D_{9} the the class corresponding to the cumulative frequency in which 2n/10 or 9n/10 lies

h = class interval size of the class

f = frequency of the class containing D_{2} or D_{9}

n = number of values, or the total frequency.

C.F = cumulative frequency of the class preceding the class containing D_{2} or D_{9}

__Percentiles:__

The values which divide an array into one hundred equal parts are called percentiles. The first, second, Ninety-ninth percentile are denoted by P1, P2,........P_{99.} The 50th percentile P_{50} corresponds to the median. The 25th percentile (P_{25)} corresponds to the first quartile and the 75th percentile (P_{75)} corresponds to the third quartile.

__Percentiles for Ungrouped Data:__

Percentile from ungrouped data could be calculated from the following formulae;

__Percentiles for Grouped Data:__

Percentiles can also be calculated for grouped data which is done with the help of following formulae;

Where,

l = lower class boundary of the class containing the P_{35} or P_{99} , i.e. the class corresponding to the cumulative frequency in which 35n/100 or 99n/100 lies

h = class interval size of the class containing. P_{35} or P_{99}

f = frequency of the class containing P_{35} or P_{99}

n = number of values, or the total frequency.

C.F = cumulative frequency of the class preceding the class containing P_{35} or P_{99 }