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SSC GD Constable Mean, Median, Mode

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This page covers SSC GD Constable 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

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

Practice 2easy

The mean of four numbers is 20. If three of the numbers are 16, 18, and 22, what is the fourth number?

Practice 3easy

The ages of 6 employees are: 22, 25, 28, 25, 30, 25. What is the mode of their ages?

Practice 4easy

The median of the dataset 5, 9, 3, 7, 11, 13, 1 is:

Practice 5easy

The mean of 8 numbers is 15. If the sum of the first 5 numbers is 70, what is the sum of the remaining 3 numbers?

Practice 6medium

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 7medium

The median of five consecutive even numbers is 16. What is the sum of the largest and smallest numbers in this set?

Practice 8medium

A dataset has the following values: 5, 8, 8, 12, 15, 8, 20. What is the mode of this dataset?

Practice 9medium

The mean of 10 numbers is 35. If the mean of the first 6 numbers is 30 and the mean of the last 5 numbers is 40, what is the 6th number (which is counted in both groups)?

Practice 10medium

The mean of a set of 12 numbers is 48. When a new number is added, the mean becomes 50. What is the new number?

Practice 11hard

In a dataset of 10 numbers arranged in ascending order, the median is 25. When a new number 45 is added and the dataset is re-arranged, the median of the 11 numbers becomes 28. What must be true about the original 6th value?

Practice 12hard

A set of 15 observations has a mean of 32. When two observations are removed, the mean of the remaining 13 observations becomes 30. What is the sum of the two removed observations?

Practice 13hard

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

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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