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IBPS Clerk Mean, Median, Mode

Study Material — 15 PYQs (2021–2021) · Concept Notes · Shortcuts

IBPS Clerk Mean, Median, Mode is a frequently tested subtopic — 15 previous year questions from 2021–2021 papers are included below with concept notes, key rules and shortcut tricks.

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2021–2021
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Previous Year Questions

IBPS Clerk Mean, Median, Mode — Past Exam Questions

15 questions from actual IBPS Clerk papers · all shown free · click option to reveal solution

Exam Q 12021Previous Year Pattern

The ages of 7 employees are arranged in ascending order: 22, 24, 26, 28, 30, 32, 34. What is the median age?

Exam Q 22021Previous Year Pattern

The median of the dataset: 12, 18, 15, 22, 20 is ___. (Arrange in order first)

Exam Q 32021Previous Year Pattern

The marks obtained by 5 students in a test are: 45, 52, 48, 52, 63. What is the mean of their marks?

Exam Q 42021Previous Year Pattern

A dataset has values: 5, 8, 8, 8, 12, 15. The mean is 9.33 (approx). What is the mode?

Exam Q 52021Previous Year Pattern

The mean of 6 numbers is 24. If five of the numbers are 18, 22, 26, 28, and 30, what is the sixth number?

Exam Q 62021Previous Year Pattern

In a dataset of 8 values: 10, 15, 15, 20, 20, 20, 25, 30, what is the mode?

Exam Q 72021Previous Year Pattern

In a class of 30 students, the mean score is 75. In another class of 20 students, the mean score is 85. What is the combined mean score of all 50 students?

Exam Q 82021Previous Year Pattern

The mean of 8 numbers is 24. If one number is replaced by 40, the new mean becomes 27. What was the original number that was replaced?

Exam Q 92021Previous Year Pattern

The mode of a dataset is 28, and it appears 5 times. The second most frequent value is 35, appearing 3 times. If the dataset has 20 observations total, and all other values appear exactly once, how many distinct values are in the dataset?

Exam Q 102021Previous Year Pattern

Five numbers have a mean of 32. When a sixth number is added, the mean becomes 30. What is the sixth number?

Exam Q 112021Previous Year Pattern

A dataset consists of 7 numbers: 12, 15, 18, 20, 22, 25, 28. If 20 is removed and replaced with 35, what is the change in the median?

Exam Q 122021Previous Year Pattern

A dataset has 20 observations with mean 25. Another dataset has 30 observations with mean 35. When both datasets are combined, what is the mean of the combined dataset?

Exam Q 132021Previous Year Pattern

A dataset has 11 observations. When arranged in order, the median is 18. The mode is 18 (appearing 3 times). If the mean is 20, what is the sum of all 11 observations?

Exam Q 142021Previous Year Pattern

In a dataset of 9 numbers arranged in ascending order, the median is 15. If the 5th number is 15 and the 4th number is 12, what is the sum of the 6th and 8th numbers if their mean is 19?

Exam Q 152021Previous Year Pattern

A frequency distribution has 5 classes with frequencies 8, 12, 20, 15, and 5. The midpoints are 10, 20, 30, 40, and 50 respectively. What is the mean of this distribution?

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
Standard Deviation & Variance→
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