Question

determine the range and standard deviation of the prices of digital cameras shown below.

\\$160, \\$94, \\$176, \\$180, \\$95, \\$129, \\$229, \\$265

the range of the prices is \\$ 171.
(simplify your answer.)

the standard deviation of the prices is \\$ \box.
(round the final answer to the nearest cent as needed. round all intermediate values to the nearest cent as needed.)

Explanation:

Calculate the sample mean

The data set of camera prices is:

$$ \{160, 94, 176, 180, 95, 129, 229, 265\} $$

The number of data points is \(n = 8\).

$$
LATEXBLOCK0
$$

Compute the sum of squared deviations

Subtract the mean \(\bar{x} = 166\) from each data value, square the result, and sum them:

$$
LATEXBLOCK1
$$

Calculate the sample standard deviation

Using the sample standard deviation formula with \(n - 1 = 7\) degrees of freedom:

$$
LATEXBLOCK2
$$

Rounding to the nearest cent gives \(60.59\).

Answer:

Determine the range and standard deviation of the prices of digital cameras shown below.

$160, $94, $176, $180, $95, $129, $229, $265

The range of the prices is $ 171.
(Simplify your answer.)

The standard deviation of the prices is $ <blank>60.59</blank>.
(Round the final answer to the nearest cent as needed. Round all intermediate values to the nearest cent as needed.)