The following data points represent the volume of gas in each race car driver's tank (in liters).
$$
4,5,13, \text { ? }
$$

If the mean of the data set is $7 \mathrm{~L}$, find the missing volume of gas.
$\square$ $\mathrm{L}$

Question

The following data points represent the volume of gas in each race car driver's tank (in liters).
$$
4,5,13, \text { ? }
$$

If the mean of the data set is $7 \mathrm{~L}$, find the missing volume of gas.
$\square$ $\mathrm{L}$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To find the missing volume of gas, we start by using the formula for the mean of a data set. The mean $\mu$ of $n$ data points $x_1, x_2, \ldots, x_n$ is given by: $$ \mu = \frac{x_1 + x_2 + \cdots + x_n}{n} $$ In this case, the mean $\mu$ is 7 liters, and the data points are 4, 5, 13, and the unknown value $x$. ‖ ‖ step 2 ⋮ Substitute the known values into the mean formula: $$ 7 = \frac{4 + 5 + 13 + x}{4} $$ ‖ ‖ step 3 ⋮ Multiply both sides of the equation by 4 to solve for $x$: $$ 7 imes 4 = 4 + 5 + 13 + x $$ $$ 28 = 22 + x $$ ‖ ‖ step 4 ⋮ Subtract 22 from both sides to isolate $x$: $$ x = 28 - 22 $$ $$ x = 6 $$ ‖ ∻Answer∻ ⚹ The missing volume of gas is 6 liters. ⚹ ∻Key Concept∻ ⚹ Mean of a data set ⚹ ∻Explanation∻ ⚹ The mean of a data set is the sum of all data points divided by the number of data points. By rearranging the mean formula, we can solve for the missing data point. ⚹◊What is the formula to calculate the mean of a data set in statistics?⍭ Generate me a similar question◊

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