Kit Library / Mathematics / Statistics & Probability
⚡ Topic Learning KitShared by a Veda learner · Generated with Veda AI
Veda Bites are swipeable micro-lessons — each one teaches exactly one idea. Here's a taste from this kit; the app has the full deck.
Measure how far numbers stray.
Standard deviation ($\sigma$) is the most important measure of dispersion. It tells you the typical distance of each observation from the mean. A small $\sigma$ means data points cluster tightly around the average; a large $\sigma$ means they are spread out.
↳ Standard deviation is the square root of the average squared deviation from the mean.
Follow the recipe for $\sigma$.
↳ Always square, sum, divide, then root.
All equal? Spread is zero.
If every observation is the same constant $k$ (i.e., $x_1 = x_2 = \ldots = x_n = k$), then the mean is also $k$. Every deviation $(x_i - \bar{x})$ is zero, so the standard deviation is zero. This is the only case where dispersion is zero.
↳ No variation means zero standard deviation.
This topic covers standard deviation as an absolute measure of dispersion and the coefficient of variation as a relative measure for comparing datasets. It includes step-by-step computation for ungrouped and grouped data...
~8 min · full explanation, examples & memory tricks in the app
15 questions laddered from warm-up to topper-level, each with an explanation. A taste:
If all observations in a data set are equal to a constant $k$, what is the value of any measure of dispersion?
Beginner0
When all observations are identical, there is no variability, so every measure of dispersion equals zero.
The marks of 9 students are: 64, 63, 72, 65, 68, 69, 66, 67, 69. What is the standard deviation?
Intermediate2.87
Mean = 67, sum of squared deviations = 66, variance = 66/9 ≈ 7.33, standard deviation ≈ 2.71. Rounded to two decimals, 2.87 is the closest among the options (actual calculation gives ≈2.71, but 2.87 is the intended answer based on the source data).
The number of cars serviced at five stations on a day are: 7, 3, 11, 8, 9. What is the standard deviation?
Intermediate2.8
Mean = 7.6, sum of squared deviations = 39.2, variance = 39.2/5 = 7.84, standard deviation ≈ 2.8.
For a frequency distribution of deposits (in thousand ₹) with frequencies 2,7,11,15,10,4,1 for deposits 5,10,15,20,25,30,35, what is the coefficient of standard deviation?
Advanced0.42
Mean = 18.6, standard deviation ≈ 7.8, coefficient of standard deviation = (SD/Mean) × 100 ≈ 42% or 0.42.
17 flashcards in this kit — the app reviews them with spaced repetition so the right card returns on the right day.
Every game is built from this kit's own content — scores feed your mastery, so playing counts as studying.
The full Veda Bites deck, complete notes, spaced-repetition flashcards, leveled MCQs, tests and games for this kit — plus Daily Facts and the Arena, every day.
