find the range and the standard deviation of the prices of backpacks, show all work,$11.99,$8.84,$16.98,$9.99,$10.45,$10.86,$11.99

Range you should know and standard deviation, you just apply the formula for standard deviation. The formula can be found on the net.

To find the range and standard deviation of the prices of backpacks, you'll need to follow a step-by-step process. Here's how you can do it:

Step 1: List all the prices of backpacks:
$11.99, $8.84, $16.98, $9.99, $10.45, $10.86, $11.99

Step 2: Calculate the range:
The range is calculated by finding the difference between the highest and lowest values in the dataset.
Highest Value: $16.98
Lowest Value: $8.84
Range = Highest Value - Lowest Value
Range = $16.98 - $8.84 = $8.14

So, the range of prices of backpacks is $8.14.

Step 3: Calculate the standard deviation:
The standard deviation measures the amount of variation or dispersion in the dataset. Here's the step-by-step process to calculate it:

a. Find the mean (average) of the prices:
Mean = (Sum of all prices) / (Number of backpacks)
Mean = ($11.99 + $8.84 + $16.98 + $9.99 + $10.45 + $10.86 + $11.99) / 7

Adding all prices: $11.99 + $8.84 + $16.98 + $9.99 + $10.45 + $10.86 + $11.99 = $80.10
Mean = $80.10 / 7 = $11.44 (rounded to two decimal places)

b. Calculate the deviation of each price from the mean:
Deviation = Price - Mean
Deviation for each price:

$11.99 - $11.44 = $0.55
$8.84 - $11.44 = -$2.60
$16.98 - $11.44 = $5.54
$9.99 - $11.44 = -$1.45
$10.45 - $11.44 = -$0.99
$10.86 - $11.44 = -$0.58
$11.99 - $11.44 = $0.55

c. Calculate the squared deviation for each price:
Square each deviation:
($0.55)^2 = $0.30
(-$2.60)^2 = $6.76
($5.54)^2 = $30.70
(-$1.45)^2 = $2.10
(-$0.99)^2 = $0.98
(-$0.58)^2 = $0.34
($0.55)^2 = $0.30

d. Compute the variance:
Variance = (Sum of squared deviations) / (Number of backpacks)
Variance = ($0.30 + $6.76 + $30.70 + $2.10 + $0.98 + $0.34 + $0.30) / 7

Sum of squared deviations: $41.48
Variance = $41.48 / 7 = $5.93 (rounded to two decimal places)

e. Calculate the standard deviation:
Standard Deviation = square root of Variance
Standard Deviation = square root of $5.93
Standard Deviation ≈ $2.44 (rounded to two decimal places)

So, the standard deviation of the prices of backpacks is approximately $2.44.