Assignment 2: Answers to Questions

Which of the three measures of central tendency is most influenced by extreme temperature values? Why?

The mean is the most influenced by outlier temperature values because it is averaged in with all of the other temperatures. An extreme temperature, whether it be very high or very low will be accounted for when calculating the average of all the temperatures and will have an affect on that data. The median is the number in the middle of all the data, so outliers would not really influence the median as much. An extremely high or low temperature would just be added to the sequence of numbers, not having a great affect on determining what the middle number is. The mode is the number that occurs the most often, and as we know, an outlier is one that is an extreme, and does not occur very frequently.

Why might these extremes have occurred?

Extremes temperature readings may have occurred because of many reasons. Weather, exercise, showers, food or beverages consumed, stress, and sickness could lower or raise our body temperatures. It is also important to take into consideration the measuring tool being used. If it does not seem like there are already so many random events that play a role in extreme temperature findings, it is possible that a faulty thermometer could be the reason.

Are extreme values rare and unusual or not?

According to our values and most of the classes, an extreme measurement was rare. There were usually only one or two temperature readings in each group that were extreme, and were usually influenced by some factor that caused the reading to be so different. Even though extreme values may be rare and can be frustrating to account for, they help to remind us that experiments are not perfect. It is important to take into consideration all the factors that may have an affect on your findings.

How reliable do you think these extreme data values might be?

These extreme data values are not very reliable, and should sometimes even be disregarded. This is because there is often a systematic bias that occurs in order to cause the extreme data values.

Look up the article by Allen L. Shoemaker to find out the correct body temperature, why 98.6 F is incorrect, and where this value came from.

According to the article, when measuring body temperature orally, the normal temperature is 98.25 F. The common idea of 98.6 F came about one hundred years ago, by Wunderlich. According to Shoemaker, Wunderlich was inaccurate due to faulty thermometers and diurnal fluctuations. The standard deviation of temperatures according to Shoemaker is 0.73.

How does the difference of your arithmetic average temperature and the Standard Deviation compare the the SD of body temperatures given in the article? Is your body temperature average particularly unusual? Explain.

Carolyn:

97.817 + .73 = 98.547

Although 97.817 F is below the normal body temperature of 98.25 F, it is within one standard deviation of the normal temperature, and therefore my body temperature is not particularly unusual.

Kate:

98.0667 + .73 = 98.7967

My body temperature is within one standard deviation of the normal body temperature of 98.25 as well.

How representative do you think your body temperature data are?

Carolyn:

I think that my body temperature data is quite representative of the normal body temperature. Although it is slightly cooler than the normal body temperature, it is still within one standard deviation of the normal body temperature. Although research shows that men are usually cooler, I feel as though I am usually cold, and so therefore it makes sense that my temperature would be cooler rather than warmer.

Kate:

According to the math my body temperature data is fairly close to the normal body temperature. Before this project the only time I ever took my temperature was when I was not feeling well. It was interesting to find that my average body temperature is pretty close to the norm. This is something that I never would have known if I was not given this assignment.

What might affect the mean of the data?

The mean of the data is affected by outliers in the data. Although neither of us had extreme outliers, the coolest and warmest temperatures would have affected the mean, especially considering that there were not that many data points recorded in the first place.

Do you think if you took more data, you’d be more or less accurate? Why?

With the addition of more data, we think that we would definitely be more accurate. If we were to continue taking our temperature, we would find a lot more data to be within the normal range, and although we might still find outliers, they would be few and far between. As we discussed in class on January 18th, in taking the mean, each data point is given equal value. Therefore, the fewer data points, the more weight each point is given. If more data were to be taken, each point would hold less weight, and therefore outliers would not change the mean quite as much.

Take the arithmetic average of your body temperature and tell me what it is in Celsius. Tell me how you turn Fahrenheit into Celsius.

Fahrenheit is changed to Celsius by taking the Fahrenheit minus 32, and dividing that answer by 1.8.

Carolyn:

(97.817-32)/1.8 = 36.565 C

Kate:

(98.0667-32)/1.8 = 36.704 C

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