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SSC CHSL Mean, Median, Mode

Study Material — 4 PYQs (2018–2018) · Concept Notes · Shortcuts

SSC CHSL Mean, Median, Mode is a frequently tested subtopic — 4 previous year questions from 2018–2018 papers are included below with concept notes, key rules and shortcut tricks.

4 PYQs
2018–2018
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Previous Year Questions

SSC CHSL Mean, Median, Mode — Past Exam Questions

4 questions from actual SSC CHSL papers · all shown free · click option to reveal solution

Exam Q 12018Previous Year Pattern

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

Exam Q 22018Previous Year Pattern

A teacher records the test scores of 6 students: 45, 52, 48, 52, 55, 48. What is the median score?

Exam Q 32018Previous Year Pattern

The mean of five numbers is 18. Four of the numbers are 14, 16, 20, and 22. What is the fifth number?

Exam Q 42018Previous Year Pattern

The marks obtained by 5 students in a test are: 12, 18, 15, 12, and 23. What is the mean 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

26graded MCQs · easy to hard · full solution & trap analysis · showing 20 of 26

All MCQs →
Practice 1easy

The ages of 6 people are: 22, 25, 28, 30, 35, and 40 years. What is the median age?

Practice 2easy

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

Practice 3easy

A dataset has 5 values: 10, 15, 20, 25, 30. If each value is increased by 5, what is the new mean?

Practice 4easy

The following data represents the number of books read by students: 3, 5, 7, 5, 9, 5, 11. What is the mode?

Practice 5easy

A dataset has 7 observations: 10, 15, 20, 25, 30, 35, 40. If one more observation of value 25 is added, how does the median change?

Practice 6easy

The mean of 4 numbers is 25. If three of the numbers are 20, 24, and 26, what is the fourth number?

Practice 7easy

The dataset is: 7, 9, 5, 9, 3, 9, 11. What is the mode of this dataset?

Practice 8easy

The median of 6 numbers is 15. If the numbers in ascending order are: 8, 12, x, 18, 20, 24, what is the value of x?

Practice 9medium

The mean of a dataset is 25. When a number 40 is added, the new mean becomes 26. How many numbers were in the original dataset?

Practice 10medium

In a dataset of 10 numbers, the mode is 8 (appearing 4 times), and the remaining 6 numbers are all distinct and different from 8. If the sum of all 10 numbers is 95, what is the mean?

Practice 11medium

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?

Practice 12medium

A dataset contains 6 numbers: 10, 15, 20, 25, 30, and x. The mean is 22. What is the mode if x = 20?

Practice 13medium

A dataset has 12 values. The mean is 20. If three values (18, 22, 20) are removed, what is the mean of the remaining 9 values?

Practice 14medium

A dataset has 5 numbers with mean 20. Two numbers are 18 and 22. The remaining three numbers are in the ratio 2:3:5. What is the median of this dataset?

Practice 15medium

The median of five consecutive odd numbers is 15. What is the sum of the largest and smallest numbers in this set?

Practice 16medium

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

Practice 17medium

The median of the dataset {12, 18, 24, 30, 36} is found. If a new number 28 is added to this dataset, what is the new median?

Practice 18medium

In a dataset of 10 numbers, the mode is 15 (appearing 4 times), and the remaining 6 numbers are all distinct and different from 15. If the sum of all 10 numbers is 140, what is the mean?

Practice 19hard

A dataset has 5 numbers with mean 32 and median 30. If the numbers in ascending order are a, b, 30, d, e, and a + b = 48, what is the value of d + e?

Practice 20hard

In a dataset of 10 numbers, the median is 15. When a new number 25 is added, the median of the 11 numbers becomes 16. Which of the following could be true about the original dataset?

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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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