Measures of Central Tendency for SSC CGL Tier 2, Paper 2

In SSC CGL Tier 2, the Quantitative Abilities section often asks questions based on measures of central tendency. The main measures of central tendency are Mean, Median, and Mode, while Quartiles, Deciles, and Percentiles are used to split data into parts for easier interpretation. This blog explains each concept in a simple way with formulas and examples, making it easier to solve related SSC CGL Tier 2 questions accurately and quickly.s.

Mean (Arithmetic Mean)

What is Mean?
The mean is the average of a set of numbers. It gives an idea of the central value of the data.

Formula: Mean=Sum of all observationsNumber of observations\text{Mean} = \frac{\text{Sum of all observations}}{\text{Number of observations}}Mean=Number of observationsSum of all observations​

Example Table:

Observation (x)	5	8	12	15	10
Calculation

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Calculation: Mean=5+8+12+15+105=505=10\text{Mean} = \frac{5 + 8 + 12 + 15 + 10}{5} = \frac{50}{5} = 10Mean=55+8+12+15+10​=550​=10

Median

What is Median?
The median is the middle value of a data set when the numbers are arranged in ascending or descending order. If there are two middle values, take their average.

Steps to Find Median:

1. Arrange the data in order.
2. If n is odd → median = middle number
3. If n is even → median = average of two middle numbers

Example Table:

Observation (x)	4	7	9	12	15
Ordered Data	4	7	9	12	15

Median:
Middle value = 9

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Mode

What is Mode?
Mode is the value that occurs most frequently in a data set. A data set can be unimodal, bimodal, or multimodal depending on the number of repeated values.

Example Table:

Observation (x)	3	7	7	5	9	7
Frequency (f)	1	3		1	1

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Mode:
Most frequent value = 7

Formula for Grouped Data: Mode=l+f1−f02f1−f0−f2×h\text{Mode} = l + \frac{f_1 – f_0}{2f_1 – f_0 – f_2} \times hMode=l+2f1​−f0​−f2​f1​−f0​​×h

Where:

• lll = lower boundary of modal class
• f1f_1f1​ = frequency of modal class
• f0f_0f0​ = frequency of class before modal class
• f2f_2f2​ = frequency of class after modal class
• hhh = class width

Also check out Most Repeated Quantitative Aptitude Questions for SSC CGL Tier 2

What are Quartiles?
Quartiles divide a data set into four equal parts. Each part represents 25% of the data.

• Q1 (First Quartile): 25% of data lies below this value.
• Q2 (Second Quartile/Median): 50% of data lies below this value.
• Q3 (Third Quartile): 75% of data lies below this value.

Formula to find Quartiles in a grouped data set:

Quartile	Formula
Q1	Q1=L+N4−CFf×hQ1 = L + \frac{\frac{N}{4} – CF}{f} \times hQ1=L+f4N​−CF​×h
Q2	Q2=L+N2−CFf×hQ2 = L + \frac{\frac{N}{2} – CF}{f} \times hQ2=L+f2N​−CF​×h
Q3	Q3=L+3N4−CFf×hQ3 = L + \frac{\frac{3N}{4} – CF}{f} \times hQ3=L+f43N​−CF​×h

Where:

• L = lower boundary of the quartile class
• N = total frequency
• CF = cumulative frequency before the quartile class
• f = frequency of the quartile class
• h = class width

Deciles

What are Deciles?
Deciles divide a data set into ten equal parts, each representing 10% of the data.

• D1: 10% of data lies below this value
• D5: 50% of data lies below this value (also the median)
• D9: 90% of data lies below this value

Formula to find Deciles:

Decile	Formula
Dk	Dk=L+kN10−CFf×hD_k = L + \frac{\frac{kN}{10} – CF}{f} \times hDk​=L+f10kN​−CF​×h

Where:

• k = decile number (1 to 9)
• Other symbols same as quartiles formula

Percentiles

What are Percentiles?
Percentiles divide a data set into 100 equal parts, each representing 1% of the data.

• P10: 10% of data lies below this value
• P25: 25% of data lies below this value (same as Q1)
• P90: 90% of data lies below this value

Formula to find Percentiles:

Percentile	Formula
Pk	Pk=L+kN100−CFf×hP_k = L + \frac{\frac{kN}{100} – CF}{f} \times hPk​=L+f100kN​−CF​×h

Where:

• k = percentile number (1 to 99)
• Other symbols same as quartiles formula

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Key Points to Remember

Below are the key points to remember:

• Mean uses all values; median is middle value; mode is most frequent.
• For skewed data, median and mode are better than mean.
• Quick formulas and examples help solve SSC CGL questions fast.
• Quartiles, Deciles, and Percentiles help in dividing data for analysis.
• Median, quartiles, deciles, and percentiles can be solved using grouped or ungrouped data formulas.
• Questions may include finding missing values, cumulative frequency analysis, or range calculations.
• Practicing previous year SSC CGL questions on these topics helps in quick calculations during exams.

Qualified SSC CGL Tier 1? Get ready for Tier 2 Exam, check out the below blogs:

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