Seven measurements of the length of a table in centimeters are

184.7, 182.3, 182.7, 182.1, 182.2, 184.1, and 182.9.

Find the best estimate for the length of the table.

Be sure to include units!

Answer:

Seven measurements of the length of a table in centimeters are

184.7, 182.3, 182.7, 182.1, 182.2, 184.1, and 182.9.

Find the standard deviation of the measurements.

Answer:

Seven measurements of the length of a table in centimeters are

184.7, 182.3, 182.7, 182.1, 182.2, 184.1, and 182.9.

Find the uncertainty in the average of the measurements.

a. (185+182+183+182+182+184+183)/7 =

To find the best estimate for the length of the table, you can calculate the average (or mean) of the measurements. Here's how you can do it:

1. Add up all the measurements: 184.7 + 182.3 + 182.7 + 182.1 + 182.2 + 184.1 + 182.9 = 1271

2. Divide the sum by the number of measurements (which is 7 in this case): 1271 / 7 = 181.5714

So, the average length of the table is approximately 181.57 cm. Make sure to include the units (cm) in your answer.

Now, to find the standard deviation of the measurements, follow these steps:

1. Calculate the variance, which is the average of the squared differences between each measurement and the mean:

- Subtract the mean from each measurement and square the result. For example, for the first measurement: (184.7 - 181.5714)^2 = 9.96

- Repeat this process for all measurements and sum up the squared differences. In this case, the sum of the squared differences is 56.46.

2. Divide the sum of squared differences by the number of measurements minus 1 (this corrects for the sample size). For 7 measurements, the divisor is 6.

So, the variance is 56.46 / 6 = 9.41.

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

Square root of 9.41 = 3.067

So, the standard deviation of the measurements is approximately 3.067 cm.

To find the uncertainty in the average of the measurements, you can divide the standard deviation by the square root of the number of measurements. Here's how you can do it:

1. Square root of 7 (number of measurements) = approx. 2.646

2. Divide the standard deviation by the square root of the number of measurements: 3.067 / 2.646 = approx. 1.161

So, the uncertainty in the average of the measurements is approximately 1.161 cm.