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SSC MTS Mean, Median, Mode

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This page covers SSC MTS Mean, Median, Mode with complete concept notes, 14 graded practice MCQs, key points and exam-specific tips. Free to study.

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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

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Practice 1easy

A dataset has 5 values. The mean is 16 and four of the values are 12, 14, 18, and 20. What is the fifth value?

Practice 2easy

The marks obtained by 5 students in a test are: 12, 18, 15, 12, 20. What is the mean of their marks?

Practice 3easy

The median of the dataset: 8, 14, 6, 10, 12 is ___.

Practice 4easy

The mode of the following data: 5, 7, 5, 9, 5, 7, 11, 7, 5 is ___.

Practice 5easy

If the mean of 6 numbers is 24, what is the sum of all 6 numbers?

Practice 6easy

The median of 8 numbers arranged in order is the average of the 4th and 5th numbers. If the 4th number is 18 and the 5th number is 22, what is the median?

Practice 7medium

The mean of a dataset of 12 numbers is 35. After removing two numbers (28 and 42), what is the mean of the remaining 10 numbers?

Practice 8medium

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 9medium

The median of five numbers arranged in ascending order is 18. If the first number is 8 and the last number is 32, and the second number is 14, what is the fourth number if the sum of all five numbers is 90?

Practice 10medium

A dataset has mode 15, which appears 6 times. The dataset also contains the values 10, 12, 15, 15, 15, 15, 15, 15, 18, 20. How many times does the value 20 appear if the mode remains 15 and no other value appears more than 6 times?

Practice 11medium

A class of 20 students has a mean score of 72. Another class of 30 students has a mean score of 78. What is the combined mean score of all 50 students?

Practice 12hard

In a class of 20 students, the mean score is 75. The mode is 80 (appearing 5 times). If 4 students with score 80 are replaced by 4 students with score 70, what is the new mean? (Assume no other score appears 5 or more times after the change.)

Practice 13hard

A dataset has 5 numbers with median 18. If the numbers in ascending order are: 12, 15, x, 24, 28, what is the value of x? Additionally, if we add two more numbers (both equal to 18) to make 7 numbers, what is the new median?

Practice 14hard

The mean of 8 numbers is 24. If one number is replaced by 56, the new mean becomes 28. What was the original number that was replaced?

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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