NCERT Class XI Mathematics - Statistics - Solutions
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Question : 22
Total: 34
The diameters of circles (in mm) drawn in a design are given below:
Calculate the standard deviation and mean diameter of the circles.
[Hint : First make the data continuous by making the classes as 32.5 – 36.5, 36.5 – 40.5, 40.5 – 44.5, 44.5 – 48.5, 48.5 – 52.5 and then proceed.]
| Diameters | 33 - 36 | 37 - 40 | 41 - 44 | 45 - 48 | 49 - 52 |
|---|---|---|---|---|---|
| No. of circles | 15 | 17 | 21 | 22 | 25 |
Calculate the standard deviation and mean diameter of the circles.
[Hint : First make the data continuous by making the classes as 32.5 – 36.5, 36.5 – 40.5, 40.5 – 44.5, 44.5 – 48.5, 48.5 – 52.5 and then proceed.]
Solution:
| Diameters | Modified Classes | Mid values | | | | | ||
|---|---|---|---|---|---|---|---|---|
| 33 - 36 | 32.5 - 36.5 | 34.5 | 15 | - 2 | - 30 | 60 | ||
| 37 - 40 | 36.5 - 40.5 | 38.5 | 17 | - 1 | - 17 | 17 | ||
| 41 - 44 | 40.5 - 44.5 | 42.5 | 21 | 0 | 0 | 0 | ||
| 45 - 48 | 44.5 - 48.5 | 46.5 | 22 | 1 | 22 | 22 | ||
| 49 - 52 | 48.5 - 52.5 | 50.5 | 25 | 2 | 50 | 100 | ||
| 100 | 25 | 199 |
Let assumed mean (A) = 42.5
Mean
Standard deviation (σ) =
=
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