Find the standard deviation for the following grouped data. Show your work.(Use 68 for the mean!) Data IntervalFrequency42≤x&lt;54254≤x&lt;661866≤x≤7856

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TokNeekCepTdh

Answered question

2021-12-04

Find the standard deviation for the following grouped data. Show your work.(Use 68 for the mean!)

\begin{array}{cc} Data Interval & F r e q u e n c y \\ 42 \leq x < 54 & 2 \\ 54 \leq x < 66 & 18 \\ 66 \leq x \leq 78 & 56 \end{array}

Answer & Explanation

Vincent Diaz

Beginner2021-12-05Added 19 answers

Step 1
Given data:
Mean

= 68

\begin{array}{cc} Data Interval & F r e q u e n c y \\ 42 - 54 & 2 \\ 54 - 66 & 18 \\ 66 - 78 & 56 \end{array}

To find the standard deviation
Step 2
Given, Mean

= 68

\begin{array}{cc} I n t e r v a l s & M i d p o i n t X_{i} & F r e q u e n c y f_{i} & X_{i} - μ & (X_{i} - μ)^{2} & f (X_{i} - μ)^{2} \\ 42 - 54 & 48 & 2 & - 20 & 400 & 800 \\ 54 - 66 & 60 & 18 & - 8 & 64 & 1152 \\ 66 - 78 & 72 & 56 & 4 & 16 & 896 \\ 76 & 2848 \end{array}

To find the standard deviation:

N = 76

\sum {f (X_{i} - μ)}^{2} = 2848

σ = \sqrt{\frac{\sum {f (X_{i} - μ)}^{2}}{N}}

= \sqrt{\frac{2848}{76}}

= 6.1215

The standard deviation is 6.1215.

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