Construct histogram and frequency polygon from the following data :
| Marks | Frequency |
|---|---|
| 0—10 | 5 |
| 10—20 | 10 |
| 20—30 | 15 |
| 30—40 | 18 |
| 40—50 | 8 |
OR
Explain the meaning of Sampling Survey. What are its advantages ?
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Start your 14-day free trial to unlock the full solution →Since every class is continuous and of equal width (10), the histogram is drawn with adjoining bars whose heights equal the actual frequencies, and the frequency polygon is obtained by joining the midpoints of the tops of these bars (plus two zero-frequency points at each end) with straight lines.
Step 1 — Since the classes are already continuous with equal width (10), no adjustment to frequencies is needed; bar height = class frequency directly.
| Marks (class, exclusive) | Frequency | Class midpoint |
|---|---|---|
| 0–10 | 5 | 5 |
| 10–20 | 10 | 15 |
| 20–30 | 15 | 25 |
| 30–40 | 18 | 35 |
| 40–50 | 8 | 45 |
Step 2 — Constructing the histogram. Mark 'Marks' on the X-axis (class boundaries 0, 10, 20, 30, 40, 50) and 'Frequency' on the Y-axis. For each class, draw a rectangle whose base is the class width (0–10, 10–20, …, 40–50) and whose height equals its frequency (5, 10, 15, 18, 8). Since the classes are continuous and exclusive, the rectangles are drawn touching each other with no gaps, giving five adjoining bars of heights 5, 10, 15, 18 and 8.
Step 3 — Constructing the frequency polygon. Take the midpoint of each class (5, 15, 25, 35, 45) and plot a point at a height equal to that class's frequency: (5, 5), (15, 10), (25, 15), (35, 18), (45, 8). To close the figure on the X-axis, add one imaginary class of zero frequency immediately before the first class (i.e., −10 to 0, midpoint −5, frequency 0) and one immediately after the last class (50 to 60, midpoint 55, frequency 0). Join all these points — (−5, 0), (5, 5), (15, 10), (25, 15), (35, 18), (45, 8), (55, 0) — in order, using straight lines. (A frequency polygon can equally be drawn directly on top of the histogram, by joining the midpoints of the top of each bar.)
Shape read from the data: the polygon rises steadily from the lowest class up to a peak at the 30–40 class (frequency 18), then falls for the 40–50 class — showing that marks are concentrated in the 30–40 range, with the distribution being mildly skewed rather than symmetric.
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