Lab Report On : Dowel Measurement, Probability, And, Usability

Standard deviation is a way of visualizing how spread out points of data are in a set. Using standard deviation helps to determine how rare or common an occurrence is. For example, data points falling within the boundaries of one standard deviation typically account for about 68% of data and those between (+/-)1 standard deviation and (+/-)2 standard deviations make about 27% combined. This can be better visualized by using a bell graph. Using the mean and standard deviation, the points where standard deviations occur can be drawn on the graph to better understand which data is rare and which is common.

Purpose: Weighing objects. Figuring out the density with an object by calculated volume and Archimedes’ Principle.

We know that +/- 1.96 standard deviations from the mean will contain 95% of the values. So, we can get the standard deviation by:

Standard deviation is important in comparing two different sets of data that has the same mean score. One standard deviation may be small (1.85), where the other standard deviation score could be quite large (10)(Rumsey,

Answer: The standard deviation can be calculated by subtracting the expected return from the actual return for each year and squaring the results. The squares are summed, and divided by the number of observances minus 1. The square root of that result is the standard deviation.

Standard Deviation of Mean= 0.4762Standard Deviation of Median= 0.7539The standard deviation of the Mean is smaller, which means all of the data points will tend to be very close to the Mean. The Median with a larger Standard Deviation will tend to have data points spread out over a large range of values. Since the Mean has the smaller value of the Standard Deviations, it has the least variability.

Weight 10 dry Post-82 pennies which get 24.91g, using 30ml initial volume measuring the volume of 10 pennies, record the data 3.2ml. Using equation Density= Mass/Volume, get the density of the post-82 pennies is 7.78g/ml. Then calculate the error%=0.04%, and the deviation%=1.60%.

Standard Deviation for the mean column is 0.476Standard Deviation for the median column is 0.754Standard deviation for the mean column has least variability

The coefficient of variation is in the “fair” range for data consistency, for all quartiles except the top quartile which is in the “good” range. (Gardner, 2012)

Introduction: Accuracy and precision were the major aspects of the lab. Accuracy is how close the average of the measured values are to the actual value. Precision is the closeness of repeated measurements. In the lab, the aim was to get as close as possible with both accuracy and precision when determining the mass and volume of the spheres. The mass was determined by weighing the spheres on the Analytical Scale and Triple Beam Balance Scale. The volume is determined by measuring with a ruler and by water displacement. The standard

As shown above, volume variance was derived by multiplying standard fixed cost/tonne with the difference between actual production and standard production.

Surface area is a two-dimensional measurement, and is proportional to the square of its length.

The data in Column A of the provided spreadsheet was split at the semi-colon, with the number to the left of the semi-colon representing U and the number to the left representing V. V values were entered by hand into a newly created column and were deleted from Column A. Both columns were summed, and sum totals were divided by 116 (the number of data points) to achieve means. Columns were also created for U^2 and U*V; the sum function was also used to total these columns and means were derived by dividing the sum by 116. a was calculated as 1094.04 using the following formula:

These represent the range of the sale price. Lastly, I used the formula to get the standard deviation 48,945.28, which measures the variability.

Furthermore, the measurements from a wooden block and a metal object were taken to calculate their volume and density. In this case, the calculations were more precise but due to other sources of errors, which may be systematic, random or personal, the data was not 100% accurate. There are always certain uncertainties associated with any type of measurement and it is important to know that no measurement will be one hundred percent correct.