1.64 mm/day. To find this answer, I found the average length of hair each day. I then subtracted the length of the average hair of the previous week. After this, I added all the differences together(leaving out the negative one from the last week) and found the average. That is how i did it.
We plotted all the points and then used a TI-83 to calculate the line of best fit (y= .4926x - .1231). The slope equaled 0.4926 which is the average daily beard growth rate.
Mrs. Ratliff's Class
First I found the average length of the beard hairs in millimeters for each day. Then I found the rate of growth from the previous day using the rate of change formula. I then took the average of the rates of change, which is .5485 mm of growth per day. Yay!
First I took the differences between the data entry and the previous, then took the average difference for that interval. Then i took all the averages and averaged them together, dividing by 2 to get the daily average of .385mm per day.
10/4: 3.5, 3.0, 3.0
10/6: 5.0, 5.0, 4.5
differences: (1.5, 2, 1.5)/3=average difference: 1.66/2= average growth per day
OK, here are my comments on each method.
Josh - great job making a quick estimate. As a scientist, though, I would like to see you use all the data given; it seems as if you are using only a single data point (the longest hair, on the last day) to derive your answer. However, it does come very close to what I believe is the true rate.
Jack - your answer of 1.64mm per day seems high. The rate of change formula should be the (change in length)/(change in time) for each interval. It sounds as if you averaged the differences in length, but did not account for the change in time for each one.
Sydney - your method sounds similar to Jack's, though your answer is much closer to what I would expect - sounds like you applied the rate of change formula perfectly!
Austin - your average sounds a little low. It sounds like you took the differences between the data entries in the order I gave them - which would be great if we were comparing the same object each time, for example, a plant as it grows. But unfortunately my measurements were all on different objects each time - I had to cut off the hair to measure it, so we're looking at a new object.
Though I liked Sydney's method, I must say as a scientist that I prefer the method that Richard, Brannon, and Heather did, in which they plotted data points and found a linear fit. This is how I have my students analyze their data, using software called Logger Pro. Excellent job! I wonder, can you explain the physical meaning of the y intercept? Can you explain why you think a linear fit is appropriate for this analysis?
Mrs. Ratliff, I think your students did great! By my reckoning, the winners are Richard, Brannon, and Heather - I think their method would be the best way to analyze the real data I send to you all from the South Pole. I also would give honorable mentions to Sydney and Josh for coming very close. Thank you all for taking a stab at analyzing some complex data! I will send a penguin to you all when I get back.
So what do you all expect from this experiment - will my facial hair grow faster/slower/the same at the pole? why do you think that? all I know is, I hope it will be less itchy! :)
While it may still be itchy, it seems that it would serve its original function of keeping your chin warm in the cold weather. It will probably not feel as warm because the air around you will, in general, be colder that in your town, but you should notice your chin growing slowly warmer as you spend more time in Antarctica.
I like to know the rate in INCHES per day, a unit of measurement that I can relate to...
Here in the US, we are definitely more familiar with inches (and feet, and pounds, and miles, etc), since we've grown up with those units. But I'm glad the students did their calculations using metric units, since generally science uses SI Units such as meters and kilograms. And worldwide, almost every country uses some version of the metric system. Because of that, it is handy to know how to convert between metric units (for science and the rest of the world) and US customary units (because we can relate to them). You can easily convert from inches to meters, and vice versa:
1 in = .0254 m
1 in = 2.54 cm
1 in = 25.4 mm.
That said, consider this: according to the CIA World Factbook, the only three countries in the world that haven't officially adopted the SI unit system of measurement are: the United States, Liberia, and Myanmar. Not to badmouth Liberia and Myanmar, but why does the US hold stubbornly fast with two of the least-developed countries on the planet (with poor human rights records to boot) instead of joining up with the rest of the developed world?
Besides: US customary units (including inches, feet, pounds, miles, etc) are difficult to convert even within the system, while metric units are all based on multiplying by factors of 10, 100, 1000, etc. Can you calculate in your head how many centimeters in a kilometer? (100 cm/m *1000 m/km) = 100,000 cm/km - easy peazy. How many inches in a mile? (12 in/ft * 5280 ft/mi) = 63360 in/mi... can you do that in your head?
thanks for the comment! Make sure you follow Katey Shirey's expedition to the IceCube project coming up in November 2010 - she won't be growing a beard but will be doing plenty of other cool experiments.
I do not care what the scientist utilize, inches is the true American way. If the desire to utilize the French units of measures they need to to it on theor own utilization and not on my watch. They could utlize microinces, calibers, Mils, 10ths, 8th or 16ths to show hair grown, I am not interested to convert from one system to another, they should have done so when they written the article. Poor human relations at that.
1,000 microinches = 1 mil; 10 mils = a caliber; 10 calibers = 1 tenth; 10 tenth = 1 inch.
The smallest unit of weight ia a grain 7,000 grains = 1 pound; smallest unit of capacity is the minim 60 minins = 1 fluid ounce.
2 fluid ounces = 1 wineglass; 2 wineglasses = 1 fluid gill; 2 fluid gills = 1 cup; 2 cups = 1 pint; 2 pints = 1 quart; 2 quarts = pottle; 2 pottles = 1 gallon
liquid measues is based on 2
I wrote a book on english weights and measures and there are over 600 units in the U.S. System it is not as difficult as you implicated.
Metric is for the lazy.
If "Metric is for the lazy" you may also like Roman Numerals and Hieroglyphs :-)
To the moron who insists imperial is better and metric for the lazy. 600 measurements you say for imperial vs 1 very simple equation for metric;
1 kilogram of water is 1 litre occupying 1 cubic decimetre. Freezes at 0 Celsius, boils at 100 Celsius.
10 mm to the cm, 100 cm to the metre, 1000 metres to the kilometre.
1 pascal is equal to 1 newton at 1 sq metre. 1 newton is equal to 1 kg⋅m⋅s−2
7,000 Grains, 16 ounces, 14 pounds, stones, ?tons (nobody knows because there are short and long tons - why?, 12 inches, 3 feet, 22 yards, 80 chains, miles ..... should I go on?
This is why scientists use metric and EVERY developed country in the world but America.
While the US is, arguably, great again, may I remind you that it accounts for a mere 5% of the world's population. The other 95% "relates to" millimetres, centimetres and kilometres just dandy.