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THE VISUAL LEARNING STUDIO
See the idea. Understand the connection.
35 visual explanations across 29 chapters, with topic maps throughout the library.
The chapter index will grow as additional notes are prepared. Chapters shown here are a learning collection, not a claim that the entire exam syllabus is complete.
SEE IT. CONNECT IT. EXPLAIN IT.
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Ratio, Proportion and Averages — lesson overview
Ratio and proportion
A ratio compares quantities through division. If A:B = 2:3, write A = 2k and B = 3k for a common scale factor k.
Equivalent ratios have the same relative value: 2:3 = 4:6. Units must be made compatible before directly comparing quantities.
A proportion states equality of ratios. In direct proportion one quantity scales with the other; inverse proportion describes a different relationship, not merely any decrease.
Dividing a quantity
To divide ₹600 in the ratio 2:3, total parts = 5. One part = ₹120. The shares are ₹240 and ₹360.
A ratio is not automatically a percentage of the total. In 2:3, the first share is 2/5 = 40% of the whole, not 2/3 of the whole.
When ratios share a quantity, first make that shared quantity consistent before combining them.
Arithmetic mean and weighted mean
Arithmetic mean = sum of observations ÷ number of observations. If five values have mean 12, their total is 60.
Combined means require weighting by group size. Two groups of 10 and 30 students with means 50 and 70 have combined mean (10×50 + 30×70)/40 = 65.
A simple average of 50 and 70 gives 60 and is incorrect here because the groups are unequal. A mean also need not be one of the observed values.
