The law of large numbers as it affects Kyle and Joseph February 4, 2008

Kyle and Joseph feel the law of large number is seen most easily by grades. Some course you take will have many graded assignment throughout the semester. Others have a midterm, a final and a paper. In these courses where there are so few grades making a mistake on a midterm or final makes a huge impact on you final grade. One outlier caused by randomness(like personal illness, not studying, car problems,test anxiety, stress or other event) could produce a much lower grade. In a course where there are many grades taken throughout the semester(like this one) there may be outliers but they are balanced out by the other less extreme grades. This can easily be explained by the formula for standard deviation.

The big influence in all of this comes from the letter n in the denominator of the formula. This stands for the number of pieces of data. A small amount of samples will have a very small number in the denominator of this problem making each piece have lots of weight in the outcome. One outlier would exert great influence over the other pieces.The fact that these extremely large numbers will be squared makes them an even bigger problem. If many samples were taken then the other “reliable” samples would be able to balance out these outliers and give a more reasonable number. This would give a much smaller standard deviation because more of the samples would be lumped closer to the mean of the data.

Wired for Boys? February 4, 2008

When flipping a coin we found that the percentage for the mother having 3 boys in a row was about 32%. She simply had a random of event of having 3 boys in a row. If she were to have another child, the likely hood of having a girl or boy would still be at 50%.

In our samples, we got 55% tails (girls) and 45% heads (boys). This shows that our test, like many others, came up with the usual proportion of boys to girls, about 50%. If we were to perform this test again up to 10,000 times, we would again come up with percents on either side still being close to equal. Even though the chance of having a boy or a girl is still 50% each the variation would still be there however due to randomness. 

Proportion of Male Psychology Majors… February 4, 2008

In our class the proportion of males to females is 8:46, which means roughly 17.4% of the class is male. According to the encyclopedia.com article I found, 75% of the psychology majors nationwide are female (www.encyclopedia.com).

Though the proportion is somewhat the same, with there being more females to males in our class, there still seems to be a missing representation according the article. This could be accounted for with just random events of who was able to get into the class. It could also be accounted for because of Mary Washington have a higher population of females attending school here.

Oil Change problem February 4, 2008

The information provided

Miles waited=3467

Mean= 3,258

Standard deviation=223

Calculations performed

find the middle 50%- This was done by finding both the top and the bottom 25%. I found the z-score for the top and bottom 25% were +.68 and -.68 I then used the formula to calculate the values for each side of the curve.

top 25% calculation: .68(223)+3,258=3,409.64

Bottom 25%:                 .68(223)+3,258=3106.36

The top 5% was calculated much the same way with the exception of the z-score value.

                                            1.6(223)+3,258=3614.8

Response

The argument that would be that you didn’t really wait too long to change the oil in the car. The middle 50% of people change their car’s oil between 3,106.36 and 3,409.64 miles. You are very close to this number. The top 5 % of people waited 3,614.8 miles to change their oil and 3,467 is well below that mark. In addition you are less than one standard deviation from the mean. With all these points its clear that the oil change was not put off too long.

Works Cited February 4, 2008

Bailly, Matthew D., King, Alan R., McCray, Jason A.. (04/01/2005)

Gender Versus Gender-Specific Attributes of the Psychology Major. Journal of General Psychology.

Retrieved 02/04/2008, from http://www.encyclopedia.com/doc/1G1-132241867.html

Statistics by Hand… January 29, 2008

When calculating statistics with our hand calculators we got……

• Kyle
  • Mean= 97.3
  • Median= 97.8
  • Mode= 98.2
  • Standard Deviation= 1.31
  • Standard Deviation(n-1)= 1.33
  • Variance= 1.77
• Joseph
  • Mean= 97.9
  • Median= 98
  • Mode=98
  • standard deviation= .6
  • standard deviation(n-1)= .62
  • variance=.4

We noticed that there was only a slight bit of difference between what was found on our hand calculator and what was found on SPSS. We were mostly only off by hundredths of each other. This would in certain cases affect the data due to us rounding to the nearest .1 degree though.

Statistics by SPSS…. January 29, 2008

Our statistics calculated by the SPSS program…..

 

Joseph’s Calculations

 

Kyle’s Calculations

 

Measures of central tendancy and how they apply to our findings January 29, 2008

Measures of central tendancy

1.)Mean-This measure reflects a “consensus” among the data. All pieces of data get equal say in the outcome. The mean of Joseph’s data was 97.9 degrees. This came from a range of 96-99. The fact that it is closer to 99 shows that there were more pieces of data near 99. These numbers had a greater pull since there is strength in numbers. Kyle’s Data shows this as well, her mean was 97.3. This came from a data range of 92.4 – 98.5.

2.)Median- Just like a concrete barrier in the middle of two lanes on a highway the median in a data set is the exact middle score. In Joseph’s data it was 98 once again from a range of 96-99. You can easily see this is the exact middle. Kyle’s was 97.8 from a range of 92.4 – 98.5.

3.)Mode. This piece of data reflects nothing more than what piece of data was recorded most often. In Joseph’s data it was 98. This temperature occurred five times. Kyle’s was 98.2 it occurred 6 times.

Measures of data point variation

1.)Standard Deviation- This shows the average amount each guess or measurement deviated from the mean. In Joseph’s data each measurement was about .6 from the mean. With Kyle’s data each of her measurements deviated on average 1.31 from the mean. We can then utilize this to come up with an average range. You simply add one deviation for the upper end of the range and subtract one deviation from the mean for the lower end. This would give Joseph an average range of 97.3-98.5 . every measurement taken has the highest probability of falling between these numbers. This is very good information to have to predict an event.

2.)Variance- This indicates how the data is spread out. A high variance indicates lots of change between measurement. A low variance would indicate that the data is very lumped together. Joseph’s variance was .4 while Kyle’s was 1.72 This showed that her data had the most differences between measurements.

Lab 2 question responses and analysis of the data. January 29, 2008

Out of the three measure of central tendancy the mean is most vulnerable to the affect of an outlier. To demonstrate this an outlier was put into Joseph’s Data set instead of one of his measurements. A temperature reading of 102 degrees was put in place of 99 degrees. This is an amout that is five times the standard deviation of this data set Only the mean was affected median and mode stayed the same as you can see from the charts below.

Before: After:

This is because the mean is thrown off by such a larger number than the rest of the group. This no longer reflects the closest number to all because the scale has been tipped by a number that is not representative of all the data. The mode stayed the same because 98 degrees still occurred more frequently. The median was the same as well because its still the middle value. Such an extreme value like 102 could have been the result of personal illness, the reading being taken after a shower, or even a malfunctioning thermometer. These are all examples of randomness which means they aren’t reliable. We have no control over when the thermometer will malfunction or when we get sick. Taking the mean does help control this is some regards. Since these are extenuating circumstances the fact that there are fewer extreme values in a data set are kept in check because as Dr. McEwen says “there are strength in numbers”. These less extreme values have the same weight in the mean and thereby keep it more accurate that it would otherwise be.

The article clearly states that the correct average body temperature is 98.2 degrees. Joseph’s Average temperature is 97.9 which is a deviation of .3 less than the mean. The article does state however that men tend to be .1-.2 less than this number. This means that Joseph is relatively close to the average temperature. Kyle’s mean temperature however was 97.8 degrees. This shows that her temperature is .4 degrees less than the mean and showing that her temperature is relatively lower than most males. The mean of this data in the study could of been affected by the same variable that we have been talking about the last few weeks like weather, mood, food intake, and health. Adding data to the list we have already analyze would make it more accurate. You have a much larger number of sample to integrate into the mean. This would just make it more representative of your true average temperature because once again there are strength in numbers and having more measurements would control for any extreme and rare occurrences.

Converting Fahrenheit to Celsius is done by simply subtracting 32 from the Fahrenheit measure and dividing by 1.8. Joseph’s Average body temperature once again was 97.9 degrees Fahrenheit which translates to 36.6 degrees Celsius. Kyle’s mean body temperature in Fahrenheit was 97.8 degrees and converted to Celsius it was 36.5 degrees.

Sources used for Lab 2 January 29, 2008

• McEwen,B. Spring 2008. Jan 16, 2006 Psychology 261A-02 Lecture. University of Mary Washington
• Shoemaker, Allen L. What’s Normal? Temperature, Gender, and Heart Rate. Journal of Statistics Education. 4, 2 (1996)
• Celsisus to farenheit calculation: http://geography.about.com/c/ht/00/07/How_Convert_Fahrenheit_Celsius0962932698.htm