Activity: 1.3 Activity Name: Data record and Importance of Measurements
Part 1. Conversion of Measures
1. Research and list the next conversion factors:
a. 1 Meter - Angstrom
b. 1 Mile – Inches
c. 1 Meter – Feet
d. 1 Meter – Yard
e. 1 Ton – Ounce
2. Convert the next values:
155 Gallons – cm3
40 Liters – in 3
21 MegaNewtons – Dina
99 Pound (force) – Dina
3. A scientist who has been working with a research that involves a force applied during motion in liquids has come with a new kind of unit called CIDEBIA, a CIDEBIA equals to a Newton applied per meter per second for each liter, in other words:
NmLs
Of course whenever she wants to work with different groups she gets troubles with the unit translation. For this, she must give the correct value to change to the Imperial system, specifically to pound (force) per inches per second per gallon
Pound inGal s
Obtain the conversion factor.
Part 2. Statistics
Mean
The most common description of the central tendency is the mean () and is found using:i.e.
28.5, 18.75, 22.9, 25.4, 24.55, 23.7, 23.9,
By examination of the data the mean can be estimated at around 24. Using the above equation, it is:
Median
However, the mean can distort the picture if there are a few extreme but legitimate values (not affected by inaccurate measurements). The median can help with this scenario and is found by locating the "middle" value.
22.9 23.723.924.55 25.4 28.5
Ifnis an even number the median is the mean of the two middle values.
Mode
This is the value that occurs most often and does not exist in many data sets including the one above. It is of use where the above two parameters cannot be found; most often in categorized data sets i.e. from the following pitfall trap data
Coleoptera / Molluscs / Annelids / Mammals / Dipterans / Homoptera / Hemiptera35 / 12 / 14 / 2 / 25 / 17 / 20
The mean for each category is already displayed and the median is irrelevant. The mode is the Coleoptera group with 35 hits.
Measures of Dispersion and Variability
We can describe data more fully using other parameters that are also used in the hypothesis tests.
Range- the highest and lowest value in a data set 18.75 - 28.5 and 2 - 35 respectively in the above data sets
Standard Deviation (s) - Useful to assess how variable a sample is. But the coefficient of variation is easier to use.
Coefficient of Variation- Useful to see how much variation occurs within your data set. The higher it is the more data points you need to collect to be confident that the sample is representative of the population. It can also be used to compare variation between data sets. Calculated using:wheresis standard deviation.
Variance (s2) - This is the most difficult value to use and need only be considered when using t-tests or ANOVA. Two or more s2 values can be compared statistically using the F-test or homogeneity of variance tests.
Standard Error (SE)- This is essential to assess how closely your sample relates to the population. By calculating the 95% confidence intervals () you can say that the population mean has a 95% chance of being within this range. Such information should be included in graphical output.
Standard Deviation
The Standard Deviation is a measure of how spread out numbers are.
Its symbol is σ (the greek letter sigma)
The formula is easy: it is the square root of the Variance. So now you ask, "What is the Variance?"
Variance
The Variance is defined as:
The average of the squared differences from the Mean.
To calculate the variance follow these steps:
· Work out the Mean (the simple average of the numbers)
· Then for each number: subtract the Mean and square the result (the squared difference).
· Then work out the average of those squared differences. (Why Square?)
Example
You and your friends have just measured the heights of your dogs (in millimeters):
The heights (at the shoulders) are: 600mm, 470mm, 170mm, 430mm and 300mm.
Find out the Mean, the Variance, and the Standard Deviation.
Your first step is to find the Mean:
Answer:
Mean = / 600 + 470 + 170 + 430 + 300 / = / 1970 / = 3945 / 5
so the mean (average) height is 394 mm. Let's plot this on the chart:
Now, we calculate each dogs difference from the Mean:
To calculate the Variance, take each difference, square it, and then average the result:
So, the Variance is21,704.
And the Standard Deviation is just the square root of Variance, so:
Standard Deviation:σ = √21,704 = 147.32...=147(to the nearest mm)
And the good thing about the Standard Deviation is that it is useful. Now we can show which heights are within one Standard Deviation (147mm) of the Mean:
So, using the Standard Deviation we have a "standard" way of knowing what is normal, and what is extra large or extra small.
Rottweilers are tall dogs. And Dachshunds are a bit short ... but don't tell them!
Exercise Measure the height and width of m&ms.
Materials: 2 bags of peanut m&m, ruler, string, calculator, plastic container
1- Measure the height of at least 40 m&ms and write them down.
2- With a string measure the width of each m&m.
3- Count every color of the m&m and place them in groups for analysis.
4- Analyze the height of each m&m and calculate the mode, median and mean for the height and width.
Mean for heightMedian for height
Mode for height
Mean for width
Median for width
Mode for width
5- Choose height or width and calculate the Standard Deviation and Variation. Show your work.
Standard DeviationVariation
Keep Practicing. Take data from your classmates that could be: shoe size, height, circumference of the waist, or any other easy to measure characteristic. Calculate media, mode, mean, standard Deviation and Variation.
MeanMedian
Mode
Standard Deviation
Variation