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SSC CPO Mean, Median, Mode

Study Material — 8 PYQs (2020–2020) · Concept Notes · Shortcuts

SSC CPO Mean, Median, Mode is a frequently tested subtopic — 8 previous year questions from 2020–2020 papers are included below with concept notes, key rules and shortcut tricks.

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Previous Year Questions

SSC CPO Mean, Median, Mode — Past Exam Questions

8 questions from actual SSC CPO papers · all shown free · click option to reveal solution

Exam Q 12020Previous Year Pattern

In the dataset {3, 7, 7, 9, 11, 7, 13, 15}, what is the difference between the mode and the median?

Exam Q 22020Previous Year Pattern

The median of {10, 14, 18, 22, 26, 30} is:

Exam Q 32020Previous Year Pattern

In a dataset {5, 8, 8, 12, 15, 8, 20}, the mode is:

Exam Q 42020Previous Year Pattern

Seven students scored: 45, 52, 48, 52, 55, 52, 60. What is the mean score?

Exam Q 52020Previous Year Pattern

The median of the dataset {12, 15, 18, 21, 24} is:

Exam Q 62020Previous Year Pattern

A dataset contains 7 numbers. The mean is 24. If one number is removed, the mean of the remaining 6 numbers becomes 22. What is the removed number?

Exam Q 72020Previous Year Pattern

A frequency distribution has mode 32, and the modal class is 30–40. If the frequency of the modal class is 18, the frequency of the class 20–30 is 12, and the frequency of the class 40–50 is 10, what is the approximate mean of the distribution (assuming uniform distribution within classes)?

Exam Q 82020Previous Year Pattern

A dataset has 20 observations with mean 50. The observations are divided into two groups: Group A (12 observations, mean 48) and Group B (8 observations, mean unknown). What is the mean of Group B?

Concept Notes

Mean, Median, Mode— Rules & Concept

Core ConceptRead this first — the foundation of the topic

Mean, Median, and Mode are measures of central tendency. They help us find the 'center' of a data set. Think of them as different ways to represent what's typical in a group of numbers. Mean (Average): Add all values and divide by the count.

Formula: Mean = Sum of all values / Number of values. Mean is sensitive to extreme values (outliers). If one value is very high or low, it affects the mean significantly. Median (Middle Value): Arrange data in ascending order and find the middle value.

For odd number of values: Middle value is the median. For even number of values: Average of two middle values is the median. Median is not affected by extreme values. Mode (Most Frequent): The value that appears most often in the data set.

A data set can have no mode (all values appear once), one mode (unimodal), two modes (bimodal), or multiple modes. **

Exam PatternsWhat examiners ask — read before attempting PYQs

: SSC CGL typically asks: Calculate mean/median/mode from given data, Find missing values when mean is given, Compare measures of central tendency, Problems on combined mean of groups, Frequency distribution problems. Key Shortcut for Mean: For consecutive numbers, mean = (First + Last) / 2. For arithmetic progression, mean = middle term.

Worked ExampleSolve this step-by-step before moving on

: Find mean, median, and mode of: 12, 15, 18, 15, 20, 24, 15. Step 1 - Mean: Sum = 12 + 15 + 18 + 15 + 20 + 24 + 15 = 119. Number of values = 7. Mean = 119/7 = 17. Step 2 - Median**: Arrange in order: 12, 15, 15, 15, 18, 20, 24.

Middle position = (7+1)/2 = 4th position. Median = 15. Step 3 - Mode: 15 appears 3 times (most frequent). Mode = 15. **

ShortcutsUse these to save 30–60 seconds per question

for Median: Position formula - For n values, median position = (n+1)/2. If this gives a decimal, take average of values at floor and ceiling positions. Combined Mean Formula: When two groups combine, New Mean = (n1×M1 + n2×M2) / (n1+n2), where n1, n2 are group sizes and M1, M2 are their means.

Exam TrapsCommon mistakes students make — avoid these

**: Students often forget to arrange data in order before finding median. Another error is assuming mode exists in every dataset - sometimes no value repeats. For mean, watch out for problems mixing different units or asking for weighted averages.

Key Points to Remember

  • Mean = Sum of all values ÷ Number of values
  • Median is the middle value when data is arranged in order
  • Mode is the most frequently occurring value in the dataset
  • For even number of values, median = average of two middle values
  • Mean is affected by extreme values, median is not
  • Combined mean = (n1×M1 + n2×M2) ÷ (n1+n2)
  • For consecutive numbers, mean = (first + last) ÷ 2
  • Median position for n values = (n+1) ÷ 2

Exam-Specific Tips

  • For arithmetic progression, mean equals the middle term
  • A dataset can have zero, one, or multiple modes
  • Median divides the dataset into two equal halves
  • Sum of deviations from mean is always zero
  • Mode is the only measure that can be used for categorical data
  • In a normal distribution, mean = median = mode
  • Weighted mean formula: Σ(wi × xi) ÷ Σwi

60-Second Revision — Mean, Median, Mode

  • Remember: Always arrange data in ascending order for median
  • Formula: Combined mean = (n1M1 + n2M2)/(n1+n2)
  • Trick: For consecutive numbers, mean = (first+last)/2
  • Trap: Mode may not exist if no value repeats
  • Quick: Median position = (n+1)/2 for n values
  • Alert: Mean changes with outliers, median doesn't
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