Question

prices of silver and tin the data show the price of silver and the price of tin over a recent 9 - year period. round your answers to two decimal places. silver tin 23.7 13.6 31.89 12.73 35.66 15.4 23.7 12.4 14.11 8.75 15.4 11.89 13.87 8.19 11.67 5.51 7.2 4.91 send data to excel part 1 of 3 find the standard deviation of the price of silver. the standard deviation of the price of silver is $9.62. part: 1 / 3 part 2 of 3 find the standard deviation of the price of tin. the standard deviation of the price of tin is $□.

Explanation:

Step 1: List the tin prices

The prices of tin are: \(13.6, 12.73, 15.4, 12.4, 8.75, 11.89, 8.19, 5.51, 4.91\)

Step 2: Calculate the mean (\(\bar{x}\))

First, sum the values:
\(13.6 + 12.73 + 15.4 + 12.4 + 8.75 + 11.89 + 8.19 + 5.51 + 4.91\)
\(= 13.6 + 12.73 = 26.33\); \(26.33 + 15.4 = 41.73\); \(41.73 + 12.4 = 54.13\); \(54.13 + 8.75 = 62.88\); \(62.88 + 11.89 = 74.77\); \(74.77 + 8.19 = 82.96\); \(82.96 + 5.51 = 88.47\); \(88.47 + 4.91 = 93.38\)

There are \(n = 9\) data points.
Mean \(\bar{x} = \frac{93.38}{9} \approx 10.3756\)

Step 3: Calculate squared deviations

For each data point \(x_i\), compute \((x_i - \bar{x})^2\):

• \((13.6 - 10.3756)^2 \approx (3.2244)^2 \approx 10.396\)
• \((12.73 - 10.3756)^2 \approx (2.3544)^2 \approx 5.543\)
• \((15.4 - 10.3756)^2 \approx (5.0244)^2 \approx 25.244\)
• \((12.4 - 10.3756)^2 \approx (2.0244)^2 \approx 4.098\)
• \((8.75 - 10.3756)^2 \approx (-1.6256)^2 \approx 2.642\)
• \((11.89 - 10.3756)^2 \approx (1.5144)^2 \approx 2.293\)
• \((8.19 - 10.3756)^2 \approx (-2.1856)^2 \approx 4.777\)
• \((5.51 - 10.3756)^2 \approx (-4.8656)^2 \approx 23.674\)
• \((4.91 - 10.3756)^2 \approx (-5.4656)^2 \approx 29.873\)

Step 4: Sum the squared deviations

Sum these values:
\(10.396 + 5.543 + 25.244 + 4.098 + 2.642 + 2.293 + 4.777 + 23.674 + 29.873\)
\(= 10.396 + 5.543 = 15.939\); \(15.939 + 25.244 = 41.183\); \(41.183 + 4.098 = 45.281\); \(45.281 + 2.642 = 47.923\); \(47.923 + 2.293 = 50.216\); \(50.216 + 4.777 = 54.993\); \(54.993 + 23.674 = 78.667\); \(78.667 + 29.873 = 108.54\)

Step 5: Calculate variance (\(s^2\))

Variance for sample (since we have a sample of 9 years) is \(\frac{\sum (x_i - \bar{x})^2}{n - 1}\)
\(s^2 = \frac{108.54}{9 - 1} = \frac{108.54}{8} = 13.5675\)

Step 6: Calculate standard deviation (\(s\))

Standard deviation is the square root of variance:
\(s = \sqrt{13.5675} \approx 3.68\) (rounded to two decimal places)

Answer:

\(3.68\)