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(C) To find the standard deviation,we first calculate the midpoints $(y_i)$ and use the assumed mean method $(A = 25)$:            Class      $f_i$

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$9$

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(C) To find the standard deviation,we first calculate the midpoints $(y_i)$ and use the assumed mean method $(A = 25)$:            Class      $f_i$      $y_i$      $d_i = y_i - 25$      $f_i d_i$      $f_i d_i^2$              $0-10$      $1$      $5$      $-20$      $-20$      $400$              $10-20$      $3$      $15$      $-10$      $-30$      $300$              $20-30$      $4$      $25$      $0$      $0$      $0$              $30-40$      $2$      $35$      $10$      $20$      $200$              Total      $N = 10$      -      -      $\sum f_i d_i = -30$      $\sum f_i d_i^2 = 900$      The variance $(\sigma^2)$ is given by:$\sigma^2 = \frac{\sum f_i d_i^2}{N} - \left( \frac{\sum f_i d_i}{N} \right)^2$$\sigma^2 = \frac{900}{10} - \left( \frac{-30}{10} \right)^2$$\sigma^2 = 90 - (-3)^2 = 90 - 9 = 81$Therefore,the standard deviation $\sigma = \sqrt{81} = 9$.

What is the standard deviation of the following series?

Class $0-10$ $10-20$ $20-30$ $30-40$

Frequency $1$ $3$ $4$ $2$

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What is the standard deviation of the following series? Class $0-10$ $10-20$ $20-30$ $30-40$ Frequency $1$ $3$ $4$ $2$