Introduction to statistics

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Question

Find the standard deviation for the following data:

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Solution

$\begin{aligned} N = 30, \sum_{i = 1}^{7} f_{i} x_{i} = 420, \sum_{i = 1}^{7} f_{i} {(x_{i} - \bar{x})}^{2} = 1374 \\ Therefore, \bar{x} = \frac{\sum_{i = 1}^{7} f_{i} x_{i}}{N} = \frac{1}{30} \times 420 = 14 \end{aligned}$
$Hence, variance (σ^{2})$
$= \frac{1}{N} \sum_{i = 1}^{7} f_{i} {(x_{i} - \bar{x})}^{2} = \frac{1}{30} \times 1374 = 45.8$
$and Standard deviation (σ) = \sqrt{45.8} = 6.77$

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Introduction to statistics

Remember concepts with our Masterclasses.

Find the standard deviation for the following data:

N=30,∑i=17 fixi=420,∑i=17 fixi−x¯2=1374 Therefore, x¯=∑i=17 fixiN=130×420=14 Hence, variance σ2=1N∑i=17 fixi−x¯2=130×1374=45.8 and Standard deviation (σ)=45.8=6.77

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