A Calculator can Come in Handy

Since my math class has been about statistics for the past few weeks, my whole class participated in an activity to test our knowledge. Our activity was to list the total dollars spent this semester for textbooks. Each student would write it on the white board and I was surprised on the variation. One student asked, ¨I didn't buy any, do I still go up?¨ It is very important to consider each data point in order to have an accurate sample even if the data entry is 0.

We then had to find the mean, standard deviation, median, mode, the lowest money spent, and the highest money spent. Luckily, calculators can also calculate these statistics. We all used the calculators and ended up having $243.86 as the average amount spent, but the standard deviation is $136.53. Since the standard deviation is pretty high the data varied greatly, meaning it may be best to look at either mode or median. In the end, the median was $225 and $350 for the mode. If we wanted to find an accurate sample, we would have to find more Mesa Community College students to participate. If you want to know how to calculate them in the calculator here is a link that gives you directions and meanings.

The average always needs the standard deviation?

In statistics, the mean is always reported with the standard deviation. It is important to know the standard deviation in order to analyze the data. Now, what is standard deviation? Well it is the mean of the mean. Another way of explaining is that it measures how spread out the data is. For statisticians, the standard deviation determines if the experiment or the benefits works. For example, when conducting a research about the social behaviors of a person in an awkward situation, the psychologist would write down the data they received. With that information, they calculate the average of how people react in that sample. Once they find the average, they have to calculate the standard deviation to see if their predictions were correct or false.

When calculating the standard deviation by hand, we need to find the variance based off the mean. Variance is the measure of how far the numbers are from each other. In this website, it shows and how to calculate the variance and the standard deviation (sd). What is really important to understand is, the higher the sd is, the more spread out the data is, therefore most likely not accurate or not good depending in the situation. One example could be grades from a classroom test. If the average of the test was an seventy and the sd was a 10, it means that most of the scores were in between 60 and 80. This range is not very good considering that some really understand, but some might only understand the concept.

Mean, Mode, Range, and Median?

In my class we reviewed vocabulary and concepts that are used in statistics: Mean, median, mode, and range. When I was younger I would make shortcuts to remember what each meant. Mean was the meanest out of the four because it would make me do the most work. Median would mean middle because the meaning is in the word. Mode would stand for most. Then Range would mean the distance just like a shooting range.

However, I didn't realize that in certain situations it is better to use one rather than all of them. In class we did an activity as a class and the teacher made a dot plot out of the data of the class. We saw that 8 was the mode and the median, but the mean was 9. Right now those numbers seem insignificant, but it would make a tremendous difference if it involved money. If I had a shoe business, I would look at the mode because I would be able to see from the sample that many people have size 8 shoes. Then I would make my shoe factory make the shoes, but I would want the average of how many shoes the factory produces each day. If I had customers take a survey on how satisfy they are with the service, I would use median because numbers that are not close to the rest of the data would be eliminated, therefore generally knowing what the customers actually feel when they go to my shop.

Here is a game that can help you understand the basics of mean, median, mode, and range.

Constructing a Circle Map by hand

For about a week in my math class, we worked on statistics and probability using m&ms. We then had to construct a circle map using the class data based on the number of m&ms there were for each color. It seems like there are two ways to create a pie chart. One way of calculating is by using proportions and degrees of the circle. Then you would have to use a compass and a protractor to draw accurate sectors. Here is a link that explains more about constructing it in this manner.

The next way of constructing a circle map is drawing a bar graph with the given data. Once you are done drawing the bar graph, cut out the strips and connect them to form a circle. Then place the circle on a piece of paper to trace the circle and also draw out the sectors for each variable. It might sound weird, but this way is also mathematically correct. My hypothesis is because connecting the bars makes the circumference of the circle and each bar is the arc of the circle. Therefore, making the pie chart almost accurate. The reason I say almost is because there might be some minor errors when drawing the bars or when tracing the circle.These were the strips that my partner and I connected in order to form a circle. Ours turned out too big that my partner was able to wrap it around her arm thrice!

These were the strips that my partner and I connected in order to form a circle. Our strips turned out to be too long that my partner was able to wrap it around her arm thrice!

This is our pie graph that we made based off the strips. We had to use four white papers to construct it!

The Infamous Monty Hall

In my math class we were shown this video that introduces the Monty Hall problem. Monty Hall hosted a game show named Let's Make a Deal in 1963, and one of the big games in this show was having a contestant pick a door out of the three shown. The objective of the game was to get the car. Mathematically there is a higher chance to pick the non-car since the probability would be about 66 percent. Then Monty would show one of the doors that was a non-car. Therefore, there is a 50 percent chance of getting the car right? Wrong! So what should you do? Stay with the picked door? Or swap your door?

Try it out by clinking here and see what happens after doing this experiment nine times.

So what was your result? You should have noticed that when you switched the door you would most likely get the car and if you stayed with your door, you would end up with a goat. Why? Well no matter what, the door with the non-car will be shown. There is a less chance of picking the car first so if you swap doors you have a 66 percent of getting a car instead of staying, which if you do stay, it will make you have a 33 percent chance of getting a car. Therefore if you swap, the higher probability you will have to win the car. Now that you know, don't you want to participate in the current Let's Make a Deal?

What's the Probability I Will Win?

Have you ever been in a conflict with someone and you don't know how to solve it fairly? For example, my friend and I would always argue on who should pay for our food. Normally, people would just split the check, but not us! We were both stubborn, which meant I hated losing against her. How do we solve our problem? Easy, have three matches of rock, paper, scissors and see who two out of three!

The game is simple: Paper beats rock, rock beats scissors,and scissors beats paper. Mathematically we both have an equal chance of winning since we can pick one out of the three. However, is this game really fair?

Play this game with a friend or play Rock, Paper, Scissors against the computer 45 times. Keep track on how many times you win, lose, or tie. At the same time tally mark how many times you showed rock, paper, or scissors. Make sure your partner keeps track of theirs or if you are playing against the computer, keep track of the computer's data.
Now out of 45, make a fraction of how many times you won, lost, and tied. Who won? Was the results fair ( both of you won the same number of times)?

Well theoretically there should have been an equal amount of times of winning, losing, and tying. Since there is 1/3 of winning, 1/3 of losing, and 1/3 of tying, but why is it 1/3? Well there are a total of three choices to pick from and there are three possible outcomes.

However, we all know that we do not live in a perfect world. The activity you did earlier was the practice of experimental probability. There are multiple factors that could differ the results such as basing off what the opponent did previously or watching them closely to find patterns your partner makes when throwing a specific hand gesture. If you went against the computer you may have seen the patterns it was making.

Therefore, theoretically playing rock, paper, scissors is a fair game to play, but in reality it may or may not be depending on your luck. So make sure to know your opponent's moves since it can be crucial when paying for food.