Statistics
Uttar Pradesh Board · Class 9 · Mathematics
Flashcards for Statistics — Uttar Pradesh Board Class 9 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
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Explore the full setWhat is the main advantage of graphical representation of data over tabular representation?
Answer
Graphical representation makes data easier to understand and allows for quick visual comparisons. As the saying goes, 'one picture is better than a thousand words.' It helps in visualizing relative ch…
What are the three main types of graphical representations studied in Class 9 Statistics?
Answer
The three main types are: (A) Bar graphs, (B) Histograms (both uniform and varying widths), and (C) Frequency polygons.
Define a bar graph and list its key characteristics.
Answer
A bar graph is a pictorial representation of data where bars of uniform width are drawn with equal spacing on one axis (usually x-axis) showing the variable, while the other axis (y-axis) shows values…
What is a histogram and how does it differ from a bar graph?
Answer
A histogram is a graphical representation of grouped frequency distribution with continuous class intervals. Unlike bar graphs: (1) There are no gaps between consecutive rectangles, (2) It's used for …
In a histogram, what is the relationship between the area of rectangles and frequency?
Answer
In a histogram, the areas of the rectangles are proportional to the corresponding frequencies. When all class intervals have equal width, the heights (lengths) of rectangles are proportional to freque…
Why do we need to modify rectangle lengths in histograms with varying class widths?
Answer
When class widths vary, using original frequencies as heights gives a misleading picture because areas (not heights) should be proportional to frequencies. We modify lengths to ensure areas remain pro…
How do you calculate the modified length for a class interval in a histogram with varying widths?
Answer
Step 1: Find the minimum class size from all intervals. Step 2: Use the formula: Modified length = (Original frequency × Minimum class size) ÷ (Class size of current interval). This ensures areas rema…
A class interval 0-20 has frequency 7, and another interval 20-30 has frequency 10. If minimum class size is 10, what are the modified lengths?
Answer
For 0-20: Class size = 20, Modified length = (7 × 10) ÷ 20 = 3.5. For 20-30: Class size = 10, Modified length = (10 × 10) ÷ 10 = 10. The modification ensures proper area representation.
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