MacEwen, B. (2008, Spring Semester). Psychology 261. Class Lectures. University of Mary Washington

Table of the Standard Normal (z) distribution. (2008). SixSigma. Retrieved Febuary 4, 2008, from http://www.isixsigma.com/library/content/zdistribution.asp

Out of a hundred I got 6 times that boys came up in a row of 3. So I would have 98/6= 16.33 or 16.33%.

Proportion of Boy and Girls

• Boys = 40
• Girls = 60
• Proportion of Boys = 40%
• Proportion of Girls = 60%
• Ratio of Boys to Girls = 40:60

If I continued to flip my coin until I reached a total count of 10,000, due to the law of large numbers my percentages should even out to about 50% each.

Law of Large Numbers in My Life

I am a regular shopper. On the weekends one of my favorite things to do is so shopping. I spend different amounts of money every time that I go out. Some days I would spend only $5 or $10 on one or two things, but some days I might go a bit more and spend $100 on two or three things. It all depends on what I find and how much I like it. On the average though, I spend about $20. Reasons why that might not be right are:

1. I could spend the entire day looking around the store and not find anything. Resulting in me not spending anything. There could just be nothing on the racks that I like at that time.
2. There could be a lot of stuff on the rack and I end up buying more than i was expecting. This would result in me spending a lot more.
3. There was bad weather. Lots of times if it’s gross outside, I won’t venture to the stores, so therefore I won’t spend anything.
4. How much I spend last weekend. If I had gone a little too far the weekend before, then I might not spend as much when shopping that day.
5. There could be some things that I like that cost a lot more than what something else may cost. That would increase the amount of my end of the weekend money spent.
6. I may find a bunch of discounts, so my spending could be less than regular.

There are quite a few reasons why the numbers might change. The standard deviation formula would take how much I spent for a month and add them up and find the mean for what I would spend for a month. Then take each weekend and subtract it from the mean to get the standard deviation for that single weekend. If there was a small sample (a weekend that I bought only a few things) my variation would be a lot larger than if I had a larger sample (if I had bought lots of things).

Male Psychology Major Statistics

In our class, there are 8 females and 46 males. This means that there is about 14.8% of the class is male. According to the article on encyclopedia.com, about 25% of psychology majors are male. This proportion is slightly different. This could be that there are so many females at Mary Washington.

Dad buys the car!

The information given:Miles until oil was changed = 3467

Mean = 3258

Standard Deviation = 233

CalculationsFind the median 50% by getting rid of the top 25% and the bottom 25%

The z-score for the top and bottom 25%s is .68

Value for the side of the curve:

Top 25% – .68(223)+3,258=3,409.64

Bottom 25% – .68(223)+3,258=3,106.36

The median 50% of people didn’t change their oil until between 3,410 miles and 3,106 miles. Your score isn’t that far off from the median. You would be less than one standard deviation away from the mean.

2.  This week relates to class because it again dealt with random variation and standard deviation.

3.  My data is also posted underneath.

4.  References

Causey, A. L., Flemming, S. L., & Golden, A.  (1996).  ACAT online: a proven approach to assessment in the major.  Austin Peay State Univerisity.   collegeoutcomes.com/papers/96.htm

 Mac Ewen, B. (2008 spring semester).  Psychology 261.  Class Lectures.  University of Mary Washington. 

5.  I really liked this assignment.  I enjoyed flipping coins and felt like their was a lot of room for creativity and interpretation.  I also felt that I learned a lot more about my blog.  Although I failed and gave up on the whole graph thing, I feel like our blog got a lot of organization done.

Let’s see just how un-average I am.  Perhaps I can argue that a lot of people are in the same boat as me.  I’m going to use z-scores.

467 – 258 = 209 / 223 = .94.  I will now look up .94 to find the z-score.

.94′s z = .3264

That score isn’t going to do me well to prove my point.  I am not going to subtract that number from .5.  I get 17.36.  When arguing with my boss, I would tell him that 17.36% of the population wait longer than me to get my oil changed. 

…I don’t think this is a good argument, so I might not win.  17.36% isn’t really that significant in my eyes.  It just points out the reverse.  82.64% of the population CAN and DO get their oil changed either on time or under how long it took me, but at least I’m a little under one standard deviation away from the average of how long people wait.

 In our statistics class, there are 8 boys out of a total of 46 people.  That means that 17.39% of the class is males.  This is pretty close to the nationwide statistic.  If we had 50 people in the class, 10 guys would give us 20% males which is only 5% less than nationwide proportion.  Either way, our class has about an 8% deviation from the average (2008).  Considering that Mary Washington has more girls than boys attending school, I think our proportion is VERY good.  Perhaps if more boys went to our school, our proportion would be closer to the average.     

I choose to flip a coin too. My results were:

 Heads: 40

Tails: 60

Heads 3 times in a row: 6

I’ll do like my partner did and choose Heads as Boys and Tails as Girls.

Out of 100, I got 8 times of Heads 3 times in a row.  I am not sure if this is how to calculate the probability because I couldn’t quite understand how to do so from the assignment, but I took 98/8=12.25.  Therefore the probability is 12.25 %.

 The proportion of boys and girls:

• Boys = 46
• Girls = 54
• Proportion of Boys = 46% or .46
• Proportion of Girls = 54% or .54
• Ratio of Boys to Girls = 46:54 

Based on the law of large numbers, if i kept flipping my coin 10,000 times, my proportions of both boys and girls should even out to about 50% each (Mac Ewen 2008).  The law of large numbers explains random variation’s stability.  It is the theorem to why holding onto a stock when it suddenly goes down makes sense.  The law of large numbers knows that the stock will go right back up….eventually.

Law of Large Numbers in my life

I’m a delivery girl.  I deliver pizza to make money and get paid $5.45 hourly, but the bulk of the money I make is determined by tips.  Based on the year and a half I’ve been working there, I feel like the average tip is $3.00.  I have based my average tip on the law of large numbers.  My tips vary incredibly.  Some people don’t give any tips, some people are drunk and can give me $7.00, sometimes I might deliver 20 pizzas and get a $25.00 tip (or get a normal $3.00 tip), but for the most part, I have no idea what I’m going to get.  Some nights, I will work 3 hours and come home with $60.00; other nights, a 3 hour-shift might only yield me $20.00.  I usually go into work expecting to make $40.00 at the least.  Reasons why I could be mistaken are determined based on:

1. There are too many drivers for the night.  Sometimes we will have 7 drivers on nights such as Wednesday when we really only need 5 drivers.  If there are too many drivers, I don’t get as many runs (or deliveries).
2. There aren’t enough drivers.  The reverse is also true.  When there aren’t enough drivers, I could get a ton of deliveries.  It would be a very stressful night, but these are the nights I most enjoy because at the end, I could leave with $80.00-$100.00.
3. I just get crappy tippers.  Sometimes I can have 18 or so deliveries and only make $60.00.  On average 20 deliveries usually gives a driver $100.
4. I get a bonus tip.  These tippers rule.  Sometimes, I will randomly get someone to give me $15-$20.  I love these people.  At any rate, that will bump up how much money I take home at night.
5. It’s a slow night.  Sometimes, everyone in the world, decides not to order pizza, and I don’t get many deliveries hence much tips.
6. Bad weather.  When it rains, or snows, people order pizza.  It’s not fun driving in, but is sure fun going home afterwards (because I usually get more money). 
7. I get awesome tippers.  Sometimes, everybody tips $5.00.  I love these nights.  I could only take 10 deliveries, and come home with over $50 (I get paid mileage too).

As you can see, there are plenty of reasons why I might “make that money”, or not.  The standard deviation formula used in my example would take all my tips for a night, add them up and get the mean (Mac Ewen 2008).  Next, I would take each individual tip and subtract it from the mean to get the standard deviation of that single tip.  I would then add up all the standard deviations for each individual tip and divide by however many deliveries I took that night.  That’s how I would get my standard deviation. 

If I had a small sample (if there was a night where I only took 5 deliveries), my variation would be a lot larger than if I had a larger sample (if I had 20 deliveries, or if I took all the deliveries for the entire week and got the standard deviation).

Why is this true?

Let’s say I took 5 deliveries.  I got $4, $5, a stiff, $2, and $1.  My standard deviation would be 1.85 with an average of $2.40. 

If I took all my tips for the entire month, I would have about 100 deliveries.  I probably, in one month, would have a total of 6 stiffs.  Can you see how 1 stiff on one night would have more importance than 6 stiffs out of 100 deliveries?  That 1 stiff is going to pull my average and standard deviation way down if I only have 5 deliveries.  If I have 100 deliveries, yes, the stiffs will pull the number down, but in comparison to all the regular tips, plus the random big tips, it will balance out.  That is how the law of large numbers works.  It’s all about balance.

I chose flipping a coin for my random variation because I am not good, at all, at figuring out how to program things on calculators or computers.

In doing so I had

• 46 Heads
• 54 Tails
• 8 times that Heads was 3 times in a row

I decided to have my:

• boys=Heads
• girls=tails

I changed our theme because I wanted one with widgets.  Have you figured out how to change font size within a blog entry?

Yikes.  That was rough on Thursday.  Any idea how to make our next presentation more interesting?  Everyone looked bored out of their mind!

-Rebecca