Question
Solve the following inequations graphically in a two-dimensional plane: $y-5 x \geq 0$
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Age | 16 | 17 | 22 | 19 | 21 | 16 |
Marks | 16 | 19 | 39 | 50 | 48 | 41 |
Age | 21 | 20 | 20 | 23 | 22 | 19 |
Marks | 59 | 44 | 42 | 62 | 37 | 67 |
Age | 23 | 20 | 22 | 22 | 23 | 22 |
Marks | 45 | 57 | 35 | 37 | 38 | 56 |
Age | 17 | 18 | 16 | 21 | 19 | 20 |
Marks | 54 | 61 | 47 | 67 | 49 | 56 |
Age | 17 | 18 | 23 | 21 | 20 | 16 |
Marks | 51 | 42 | 65 | 56 | 52 | 48 |
Prepare a bivariate frequency distribution by taking class intervals 16 – 18, 18 – 20,…,etc. for age and 10 – 20, 20 – 30,…, etc. for marks.
Find
(i) marginal frequency distributions.
(ii) conditional frequency distribution of marks obtained when age of students is between 20 – 22.
$\lim _{x \rightarrow 0}\left[\frac{\sqrt[3]{1+x}-\sqrt{1+x}}{x}\right]$