Question

Find the mean absolute deviation, variance, and
standard deviation for the data set showing the price of
six different jars of pasta sauce at the grocery store:
{$2.79, $1.99, $4.29, $2.49, $2.29, $3.49}

Answer 1

If the mean of the data is 2.89, then the mean absolute deviation, variance, and standard deviation will be 0.67, 0.61, and 0.78 respectively.

What are statistics?

Statistics is the study of collection, analysis, interpretation, and presentation of data or to discipline to collect, and summarise the data.

The data set is given below.

{$2.79, $1.99, $4.29, $2.49, $2.29, $3.49}

Then the mean value of the data will be

$\mu = \dfrac{{2.79+ 1.99+ 4.29+ 2.49+ 2.29+ 3.49}}{6} \\\\\mu = \ 2.89$

Then the mean absolute deviation will be

$\rm MAD = \dfrac{1}{N} \Sigma _{i=1}^N |x_i - \mu|\\\\MAD = \dfrac{1}{6} (|2.79 - 2.89| + |1.99-2.89| + ... +|3.49-2.89|)\\\\MAD = 0.6667 \approx 0.67$

Then the standard deviation will be

$\rm \sigma = \sqrt{\dfrac{\Sigma _{i=1}^N (x_i - \mu)^2}{N} }\\\\\sigma = \sqrt{\dfrac{(2.79-2.89)^2 + (1.99 - 2.89)^2 + .... + (3.49 - 2.89)^2}{6}}\\\\\sigma = \sqrt{0.61}\\\\\sigma = 0.78$

Then the variance will be

$\sigma ^2 = (\sqrt{0.61})^2\\\\\sigma ^2 =0.61$

More about the statistics link is given below.

https://brainly.com/question/10951564

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