Interactive — Statistics

Middle class (20–30) frequency: 15

Each bar is a class; its height is the frequency. The mean = Σfᵢxᵢ / Σfᵢ uses the class marks (5, 15, 25, 35, 45). Drag the slider and watch the mean shift toward the taller bar.

Middle class (20–30) frequency: 15

The dashed line is at n/2. The first class whose cumulative frequency crosses it is the median class (highlighted). Median = l + [(n/2 − cf)/f]·h.

Modal class (20–30) frequency: 15

The tallest bar is the modal class. The crossing diagonals inside it locate the mode: Mode = l + [(f₁ − f₀)/(2f₁ − f₀ − f₂)]·h.

Middle class (20–30) frequency: 15

The "less than" ogive plots (upper limit, cumulative frequency). Drawing a line at y = n/2 across to the curve and down to the x-axis reads off the median graphically.

Skewness: 0

For a skewed distribution the three averages separate on the number line, always obeying 3 Median = Mode + 2 Mean. Slide to add skew and see them spread apart.

🏏 Cricket Scores

A batsman's average is the mean of runs; a "typical" innings is described by the median.

📚 Exam Marks

Grouped mark distributions use mean, median and mode to summarise a class's performance.

🏠 Household Income

Median income is preferred over mean because a few very high incomes skew the average.

👟 Shoe & Dress Sizes

Shops stock the modal size — the one that sells most often — to meet demand.

🌡️ Weather Data

Average rainfall and temperature over class intervals are reported using the mean.

📊 Surveys & Polls

Opinion polls group responses into intervals and report central tendency and spread.

From sports to surveys, statistics turns raw data into a single meaningful summary.