Question

Statistics

Posted 5 months ago

```
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.
$\square$ $\mathrm{L}$
```

Sign in to unlock the answer

Answer from Sia

Posted 5 months ago

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 $x$:
$7 \times 4 = 4 + 5 + 13 + x$
$28 = 22 + x$

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.

Not the question you are looking for? Ask here!

Enter question by text

Enter question by image

Unlock Smarter Learning with AskSia Super!

Join Super, our all-in-one AI solution that can greatly improve your learning efficiency.

30% higher accuracy than GPT-4o

Entire learning journey support

The most student-friendly features

Study Other Question