Shared by a Veda teacher · Generated with Veda AI · Oct 2026
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.
The shortcut everyone reaches for, and it is usually wrong.
Given two group averages, it is tempting to average them. That gives each group the same say — which is only fair when the groups are the same size.
↳ An average carries the weight of the group behind it.
One formula covers every question in this topic.
Multiply each value by its weight, add, and divide by the TOTAL WEIGHT: $\dfrac{w_1x_1 + w_2x_2 + \cdots}{w_1 + w_2 + \cdots}$.
↳ Divide by the sum of the weights, never by how many values there are.
The single commonest slip in this chapter.
Rehmat has three scores, so 3 looks like the divisor. It is not — the weights are $3 : 2 : 5$, so you divide by 10. Dividing by 3 gives 224.33, which is above every score she got.
↳ If your answer is bigger than every value, you divided by the wrong thing.
One table, and the chart you choose decides what is easy.
↳ Pick the chart from the question, not the other way round.
What the height of a stack actually is.
A stacked column stands as tall as the sum of its parts: $1940 + 1700 + 1280 + 1200 + 1770 + 535 = 8425$ for Family A.
↳ Totals are what stacking shows at a glance.
The cost of stacking, in one sentence.
Every segment above the first begins wherever the one below ended, so its length is a difference, not a height.
↳ Read the top, read the bottom, subtract.
Averaging a set of averages looks like the obvious shortcut, and it is wrong more often than it is right. It gives the correct answer only when every group is the same size; the moment the groups differ, each average has…
~45 min · full explanation, examples & memory tricks in the app
The same table can be drawn as a chart in more than one way, and the choice decides which questions become easy. Clustering by family answers questions about one household; clustering by category compares the same cost a…
~45 min · full explanation, examples & memory tricks in the app
Asking which family spends the smallest SHARE on healthcare is awkward on an ordinary stacked chart, because the columns are different heights and a share has to be judged against each one separately. Three pie charts fi…
~45 min · full explanation, examples & memory tricks in the app
170 questions laddered from warm-up to topper-level, each with an explanation. A taste:
A badminton group has 8 seniors averaging $165.5$ cm and 3 juniors averaging $149.33$ cm. What is the average height of all 11 trainees?
Beginner161.09 cm
Weight each average by its group size: $\dfrac{(165.5 \times 8) + (149.33 \times 3)}{11} = \dfrac{1772}{11} = 161.09$ cm. The value $157.42$ is what you get by averaging the two averages, which ignores that there are nearly three times as many seniors.
Why does averaging the two group averages give the wrong height for the badminton group?
BeginnerIt treats the seniors' average and the juniors' average as equally important, when there are 8 seniors and only 3 juniors
Each average carries the weight of the group behind it. Averaging the averages silently gives the 3 juniors the same say as the 8 seniors.
Jaspreet cycles 5 days a week for 3 weeks, averaging $12.8$, $15.8$ and $18$ minutes. What is her average over the 15 days?
Beginner15.53 minutes
All three weeks have the same number of cycling days, so the sizes cancel and the plain average is correct: $\dfrac{12.8 + 15.8 + 18}{3} = \dfrac{46.6}{3} = 15.53$ minutes.
Averaging a set of averages gives the correct overall average in exactly which case?
BeginnerWhen every group contains the same number of values
Putting $p = q = r$ into $\dfrac{ap + bq + cr}{p + q + r}$ gives $\dfrac{(a + b + c)p}{3p} = \dfrac{a + b + c}{3}$. The sizes cancel only when they are equal.
60 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.
