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IBPS RRB PO Mean, Median, Mode

Study Material — 2 PYQs (2022–2022) · Concept Notes · Shortcuts

IBPS RRB PO Mean, Median, Mode is a frequently tested subtopic — 2 previous year questions from 2022–2022 papers are included below with concept notes, key rules and shortcut tricks.

2 PYQs
2022–2022
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8 Key Points
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Previous Year Questions

IBPS RRB PO Mean, Median, Mode — Past Exam Questions

2 questions from actual IBPS RRB PO papers · all shown free · click option to reveal solution

Exam Q 12022Previous Year Pattern

In a dataset of 8 observations, the mode is 15 and it appears 4 times. Which of the following statements is definitely true?

Exam Q 22022Previous Year Pattern

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

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
Practice MCQs

Mean, Median, Mode — Practice Questions

14graded MCQs · easy to hard · full solution & trap analysis

All MCQs →
Practice 1easy

A dataset has 7 values: 12, 15, 18, 20, 20, 25, 30. What is the mode of this dataset?

Practice 2easy

The mean of a dataset is 50 and the sum of all values is 400. How many values are in the dataset?

Practice 3easy

The mean of 4 numbers is 32. Three of the numbers are 28, 35, and 36. If a fifth number 40 is added to the dataset, what is the new mean?

Practice 4medium

In a dataset of 12 values, the sum is 480. Three new values (20, 25, 30) are added. What is the new mean?

Practice 5medium

The mean of 8 numbers is 24. If one number is removed, the mean of the remaining 7 numbers becomes 22. What is the value of the number that was removed?

Practice 6medium

Five students scored: 45, 52, 48, 55, and 50 marks. If a sixth student scores 70 marks, by how much does the mean increase?

Practice 7medium

A dataset contains 9 values: 12, 15, 18, 12, 20, 12, 25, 18, 30. What is the mode of this dataset?

Practice 8medium

The median of 7 numbers arranged in ascending order is 28. If the numbers are: 12, 18, 24, x, 35, 42, 50, what is the value of x?

Practice 9medium

A teacher records test scores for 10 students. The mean score is 72. After discovering a marking error, one student's score of 58 is corrected to 68. What is the new mean score?

Practice 10hard

In a dataset, the mean of 15 numbers is 40. When one number is replaced by 70, the new mean becomes 42. What was the original number that was replaced?

Practice 11hard

In a dataset of 10 observations, the median is 35. When a new observation of value 50 is added, the median of the 11 observations becomes 36. What was the 6th observation (middle value) in the original dataset?

Practice 12hard

A frequency distribution has mode 45. The frequencies of classes are: [40–45): 12, [45–50): f, [50–55): 8, [55–60): 5. If the mode lies in the [45–50) class, what is the minimum value of f?

Practice 13hard

A dataset of 20 numbers has mean 50. The sum of the 10 smallest numbers is 420. If the median of the entire dataset is 48, what is the sum of the 10 largest numbers?

Practice 14hard

A dataset contains 8 numbers. Their mean is 24. If three numbers (18, 22, 26) are removed from the dataset, what is the mean of the remaining 5 numbers?

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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