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Math  /  Data & Statistics

QuestionDetermine the range and standard deviation of the prices of camping tents shown below. $109,$59,$81,$59,$212,$252,$59,$101,$130 b b. \$ 109, \$ 59, \$ 81, \$ 59, \$ 212, \$ 252, \$ 59, \$ 101, \$ 130 \text { b b. }
The range of the prices is $\$ □\square (Simplify your answer.)

Studdy Solution

STEP 1

1. The data set consists of the following prices: 109,59,81,59,212,252,59,101,130 109, 59, 81, 59, 212, 252, 59, 101, 130 .
2. The range is calculated as the difference between the maximum and minimum values.
3. The standard deviation measures the amount of variation or dispersion in a set of values.

STEP 2

1. Calculate the range of the prices.
2. Calculate the standard deviation of the prices.

STEP 3

Identify the minimum and maximum values in the data set:
Minimum value: 59 59
Maximum value: 252 252

STEP 4

Calculate the range:
Range = Maximum value - Minimum value
252−59=193 252 - 59 = 193

STEP 5

Calculate the mean of the data set:
Mean = 109+59+81+59+212+252+59+101+1309\frac{109 + 59 + 81 + 59 + 212 + 252 + 59 + 101 + 130}{9}
=10629≈118 = \frac{1062}{9} \approx 118

STEP 6

Calculate each data point's deviation from the mean and square it:
\begin{align*} (109 - 118)^2 & = 81 \\ (59 - 118)^2 & = 3481 \\ (81 - 118)^2 & = 1369 \\ (59 - 118)^2 & = 3481 \\ (212 - 118)^2 & = 8836 \\ (252 - 118)^2 & = 17956 \\ (59 - 118)^2 & = 3481 \\ (101 - 118)^2 & = 289 \\ (130 - 118)^2 & = 144 \\ \end{align*}

STEP 7

Calculate the variance (average of the squared deviations):
Variance = 81+3481+1369+3481+8836+17956+3481+289+1449\frac{81 + 3481 + 1369 + 3481 + 8836 + 17956 + 3481 + 289 + 144}{9}
=393189≈4368.67 = \frac{39318}{9} \approx 4368.67

STEP 8

Calculate the standard deviation (square root of the variance):
Standard Deviation = 4368.67≈66.06\sqrt{4368.67} \approx 66.06
The range of the prices is:
193 \boxed{193}
The standard deviation of the prices is:
66.06 \boxed{66.06}

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