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 Patterns: 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 Example: 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. Quick Trick 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. Common Mistake: 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.