Question

Justine bought supplies for a class project and brought the receipt to school. The 6 items cost:
$7.00$5.00$7.00$1.00$4.00$6.00
What was the standard deviation of the prices of the items?

If the answer is a decimal, round it to the nearest ten cents.

Answer 1

To find the standard deviation of the prices of the items, we first need to calculate the mean (average) of the prices. The prices of the 6 items are as follows:

- \( 7.00 \)
- \( 5.00 \)
- \( 7.00 \)
- \( 1.00 \)
- \( 4.00 \)
- \( 6.00 \)

### Step 1: Calculate the Mean

First, we sum up the prices:

\[
7.00 + 5.00 + 7.00 + 1.00 + 4.00 + 6.00 = 30.00
\]

Next, we calculate the mean by dividing the total by the number of items:

\[
\text{Mean} = \frac{\text{Total}}{\text{Number of items}} = \frac{30.00}{6} = 5.00
\]

### Step 2: Calculate Each Deviation from the Mean

Now, we compute the deviations of each price from the mean, and then square those deviations:

\[
(7.00 - 5.00)^2 = 2.00^2 = 4.00
\]
\[
(5.00 - 5.00)^2 = 0.00^2 = 0.00
\]
\[
(7.00 - 5.00)^2 = 2.00^2 = 4.00
\]
\[
(1.00 - 5.00)^2 = (-4.00)^2 = 16.00
\]
\[
(4.00 - 5.00)^2 = (-1.00)^2 = 1.00
\]
\[
(6.00 - 5.00)^2 = 1.00^2 = 1.00
\]

### Step 3: Calculate the Variance

Next, we sum the squared deviations:

\[
4.00 + 0.00 + 4.00 + 16.00 + 1.00 + 1.00 = 26.00
\]

Then, to get the variance, we divide by the number of items (since this is a population, we divide by 6):

\[
\text{Variance} = \frac{26.00}{6} \approx 4.3333
\]

### Step 4: Calculate the Standard Deviation

Finally, we take the square root of the variance to find the standard deviation:

\[
\text{Standard Deviation} = \sqrt{4.3333} \approx 2.08
\]

### Conclusion: Round to the Nearest Ten Cents

Rounding this to the nearest ten cents, we get:

\[
\text{Standard Deviation} \approx 2.10
\]

Thus, the standard deviation of the prices of the items is \(\boxed{2.10}\).