Statistics (Mean, Median, Mode)
View Questions of Statistics (Mean, Median, Mode)
Quantitative Aptitude - Statistics (Mean, Median, Mode)
Fundamentals First
Statistics involves the collection, analysis, and interpretation of data. Mean, Median, and Mode are the three primary measures of the 'central tendency' or 'average' of a data set.
- Mean (Arithmetic Average): The most common measure of average. It is the sum of all values divided by the number of values.
- Median: The middle value of a dataset that has been sorted in order of magnitude. It is a positional average.
- Mode: The value that appears most frequently in a dataset. It is the most popular value.
Key Formulas & Concepts
- Mean: \( \text{Mean} = \frac{\sum x}{n} = \frac{\text{Sum of all observations}}{\text{Number of observations}} \)
- Median:
- Arrange the data in ascending or descending order.
- If the number of observations (n) is odd, the Median is the \( (\frac{n+1}{2})^{th} \) term.
- If 'n' is even, the Median is the average of the \( (\frac{n}{2})^{th} \) and \( (\frac{n}{2} + 1)^{th} \) terms.
- Mode: Find the number that repeats the maximum number of times.
- Empirical Relationship (Important!): For a moderately skewed distribution, the relationship between the three is given by: Mode ≈ 3(Median) - 2(Mean).
⚡ Quick Solving Tips
- Sorting is a must for Median: The most common mistake is forgetting to sort the data before finding the median.
- Effect of Outliers: The Mean is very sensitive to extremely high or low values (outliers). The Median is much more resistant to outliers. The Mode is not affected by outliers at all.
- Multiple Modes: A dataset can have more than one mode (bimodal, trimodal) or no mode at all if all values occur with the same frequency.
✍️ Suggestions for Examinations
- The empirical formula (Mode ≈ 3 Median - 2 Mean) is a high-yield formula. It is frequently asked directly or as a way to find one measure when the other two are given.
- Understand the concept behind each measure. Questions might ask 'Which measure is best for...' (e.g., for house prices, median is better than mean because of outlier mansions).
- Double-check your counting for 'n' and be careful with the even/odd median calculation.
Topics
- Number System
- H.C.F. & L.C.M.
- Decimal Fractions
- Simplification
- Square Roots & Cube Roots
- Average
- Problems on Numbers
- Problems on Ages
- Surds & Indices
- Percentage
- Operations on Numbers
- Profit & Loss
- Ratio & Proportion
- Partnership
- Chain Rule
- Time & Work
- Pipes & Cistern
- Time & Distance
- Problems on Trains
- Boats & Streams
- Alligation or Mixture
- Simple Interest
- Compound Interest
- Logarithms
- Area
- Volume & Surface Areas
- Mensuration
- Races & Games of Skill
- Calendar
- Clocks
- Stocks & Shares
- Permutations & Combinations
- Probability
- True Discount
- Banker’s Discount
- Heights & Distances
- Odd Man Out & Series
- Algebra
- Divisibility Rules & Remainder Theorem
- Factorials & Power Cycles
- Progressions (A.P., G.P., H.P.)
- Work & Wages
- Set Theory / Venn Diagrams
- Geometry (Lines, Angles, Triangles, Polygons)
- Coordinate Geometry
- Data Interpretation
- Trigonometry
- Statistics (Mean, Median, Mode)
- Arithmetic Operations
- Quadratic Equations
Other Subjects
- Prestressed Concrete
- Fluid Mechanics
- Geotechnical Engineering
- Ground Improvement Techniques
- Groundwater Engineering
- Highway Engineering
- Hydraulics and Hydraulic Machines
- Hydrology
- Irrigation Engineering
- Open Channel Flow
- Pavement Design
- Estimation, Costing and Valuation
- Railway Engineering
- Soil Mechanics
- Strength of Materials
- Structural Analysis
- Surveying
- Traffic Engineering
- Transportation Engineering
- Wastewater Treatment
- Water Supply and Sanitation
- Contracts and Specifications
- Reasoning
- Engineering Mathematics
- Air Pollution and Control
- Bridge Engineering
- Building Materials and Construction
- Concrete Technology
- Construction Equipment
- Construction Planning and Management
- Quantitative Aptitude
- Dam Engineering
- Design of RCC Structures
- Design of Steel Structures
- Drainage Engineering
- Earthquake Engineering
- Engineering Geology
- Engineering Graphics
- Engineering Mechanics
- Environmental Engineering
- General Awareness / General Knowledge (GK)