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13.Statistics
medium
આપેલ પ્રત્યેક માહિતી માટે મધ્યક અને વિચરણ શોધો : ત્રણના પ્રથમ $10$ ગુણિત
Option A
Option B
Option C
Option D
Solution
The first $10$ multiples of $3$ are
$3,6,9,12,15,18,21,24,27,30$
Here, number of observations, $n=10$
Mean, $\bar x = \frac{{\sum\limits_{i = 1}^{10} {{x_i}} }}{{10}} = \frac{{165}}{{10}} = 16.5$
The following table is obtained.
| ${x_i}$ | $\left( {{x_i} – \bar x} \right)$ | ${\left( {{x_i} – \bar x} \right)^2}$ |
| $3$ | $-13.5$ | $182.25$ |
| $6$ | $-10.5$ | $110.25$ |
| $9$ | $-7.5$ | $56.25$ |
| $12$ | $-4.5$ | $20.25$ |
| $15$ | $-1.5$ | $2.25$ |
| $18$ | $1.5$ | $2.25$ |
| $21$ | $4.5$ | $20.25$ |
| $24$ | $7.5$ | $56.25$ |
| $27$ | $10.5$ | $110.25$ |
| $30$ | $13.5$ | $182.25$ |
Variance $\left( {{\sigma ^2}} \right) = \frac{1}{n}\sum\limits_{i = 1}^{10} {{{\left( {{x_1} – \bar x} \right)}^2} = } \frac{1}{{10}} \times 742.5 = 74.25$
$742.5$
Standard 11
Mathematics
Similar Questions
નીચે આપેલ આવૃત્તિ વિતરણનું વિચરણ શોધો.
|
$class$ |
$0 – 2$ |
$2 – 4$ |
$4 – 6$ |
$6 – 8$ |
$8 – 10$ |
$10 – 12$ |
|
$f_i$ |
$2$ |
$7$ |
$12$ |
$19$ |
$9$ |
$ 1$ |
hard
જો આપેલ આવ્રુતિ વિતરણનો વિચરણ $50$ હોય તો $x$ ની કિમત મેળવો.
| Class | $10-20$ | $20-30$ | $30-40$ |
| Frequency | $2$ | $x$ | $2$ |
