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# The mean deviation of the data 3, 10, 10, 4, 7, 10, 5 from the mean is: - (a) 2(b) 2.57(c) 3(d) 3.75

Last updated date: 18th Jun 2024
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Hint: Apply the formula for mean deviation given as: - Mean deviation = $\dfrac{1}{n}\sum\limits_{i=1}^{n}{\left| \overline{x}-{{x}_{i}} \right|}$, where ‘n’ is the number of observations, $\overline{x}$ is the mean of the given data and ${{x}_{i}}$ are the given observations where i = 1, 2, ……, n. To find the value of mean use the formula $\overline{x}=\dfrac{\sum{{{x}_{i}}}}{n}$. Substitute all the values in the above formula with n = 7 to get the required mean deviation.

Now, we know that the formula used to calculate the mean deviation is given as: - Mean deviation = $\dfrac{1}{n}\sum\limits_{i=1}^{n}{\left| \overline{x}-{{x}_{i}} \right|}$, where $\overline{x}$ is the mean of the given data, ‘n’ is the number of observations and ${{x}_{i}}$ are the given data where i = 1, 2, .….,n. So, to find the mean deviation we need to find the mean of the given data first. The mean is given by the formula: - $\overline{x}=\dfrac{\sum{{{x}_{i}}}}{n}$. On counting the number of data given to us, we conclude that n = 7. So, we get,
\begin{align} & \Rightarrow \overline{x}=\dfrac{3+10+10+4+7+10+5}{7} \\ & \Rightarrow \overline{x}=\dfrac{49}{7} \\ & \Rightarrow \overline{x}=7 \\ \end{align}
$\Rightarrow$ Mean deviation = $\dfrac{1}{7}\sum\limits_{i=1}^{7}{\left| 7-{{x}_{i}} \right|}$
$\Rightarrow$ Mean deviation = $\dfrac{1}{7}\left[ \left| 7-3 \right|+\left| 7-10 \right|+\left| 7-10 \right|+\left| 7-4 \right|+\left| 7-7 \right|+\left| 7-10 \right|+\left| 7-5 \right| \right]$
$\Rightarrow$ Mean deviation = $\dfrac{1}{7}\left[ \left| 4 \right|+\left| -3 \right|+\left| -3 \right|+\left| 3 \right|+\left| 0 \right|+\left| -3 \right|+\left| 2 \right| \right]$
$\Rightarrow$ Mean deviation = $\dfrac{1}{7}\left[ 4+3+3+3+0+3+2 \right]$
$\Rightarrow$ Mean deviation = $\dfrac{1}{7}\left[ 18 \right]$
$\Rightarrow$ Mean deviation = 2.57