Mara’s Results
Calculator
Mode: My data was tri-modal, meaning I had three modes; 95.9, 98.4, and 98.9. These are the most commonly occurring temperatures in my data.
Median: 98.55. The median is the middle number when the data are listed in ascending order. This is the middle-most number in the data.
Arithmetic Mean: 98.226. The arithmetic mean is the average of all of the temperatures. If asked to give one number to represent the person’s overall temperature, it would be the arithmetic mean.
Standard Deviation: 1.57402741. The standard deviation is the average departure from the mean.
Variance: 1.339581105
SPSS
|
N |
Valid | 34 | |
| Missing | 0 | ||
| Mean | 98.2294 | ||
| Median | 98.5500 | ||
| Mode | 95.90(a) | ||
| Std. Deviation | 1.16060 | ||
| Variance | 1.347 | ||
Multiple modes exist. The smallest value is shown.
Outlier temperatures would most affect the arithmetic mean because it is included in the calculation. The outlier would make the mean more extreme than it truly is. It wouldn’t disrupt the mode because it is unlikely to repeat many times and therefore would be disregarded. The median is a number in the middle of the data and outliers lay beyond this boundary. Therefore, they would not affect the median.
Outliers may occur because of systematic events such as taking your temperature outside. The extreme value may also be the result of faulty equipment or a random event. Either way, these events are rare and are not reliable data values. The normal curve shows that most data points should be clustered about the mean.
Randomness plays a part in creating outliers. Since randomness is not predictable, then outliers that are influenced by randomness are not reliable. 98.6 degrees F is not the correct body temperature. It is actually 98.25 degrees F. The confusion is attributed to unreliable thermometers and an insufficient account for random fluctuation. As the instrument of measure becomes more precise, our mean because more accurate. Also, the original estimate did not take into account daily fluctuations in temperature; in part, randomness.
(My arithmetic average temperature) – (Correct Average Temperature) = SD
98.226 degrees F - 98.25 degrees F = -.024 degrees F
My average was .024 degrees F colder than the average correct temperature. This is significantly closer to the correct temperature than the sample SD of .73. In other words, I am particularly average. One reason that my temperature was so close to average could be that I used a Vick’s Comfort-Flex thermometer, a $17 thermometer that is highly accurate. Overall, my data are representative. The mean of my data is probably lowered by my morning temperature, which was consistently around 95.9 F. Extending the length of the experiment would make it more accurate because of the Law of Large Numbers, which states that the more data that is used, the closer the answer will be to the mean.
98.226 degrees F= 36.792 degrees Celsius
Degrees Celsius= (Degrees Fahrenheit-32) x 5/9
Mike’s Results
My Mode was 97.3 and appeared 6 times in my data.
My median data is also 97.3F. This is the value in the direct middle of all my temperatures. Since I had only 34 data points, the median is my 17.5th point, an average of my 17th and 18th values. Since they were the same value, the median is 97.3.
The mean, my average temperature, was 97.06F
My standard deviation by calculator was .7071, which is the square root of 2 divided by 2. This is the average departure from the mean temperature.
My variance was .5
Statistics from SPSSN Valid 34
Missing 36
Mean 97.0618
Median 97.3000
Mode 97.30
Std. Deviation .70711
Variance .500
Outlier temperatures would most affect the mean, because a slight change in the algebra involved in obtaining the mean results in different values. Take for example the data set of 9, 10 and 11. The median is 10 and the mean is 10. If we throw in a 2 however, the median becomes 9 and the mean becomes 5.5. A larger change occurs in the mean, due to the more complex methods by which we obtain it.
Outliers occur mostly due to systemic events such as drinking hot tea, or eating ice cream before taking your temperature. I can clearly remember times when I did both, and without thinking directly took my temperature right after. Such times resulted in spikes in both directions, as is seen in my data. These events were rare however, but are easily explainable. Outliers are not very reliable when looking at average temperatures in such a short period, but if we were tracking temperature over a number of months, such data may be acceptable.
My average body temperature was 97.06 degrees F, while the average body temperature given by the article was 98.25 degrees F. 97.06 F – 98.25F = -1.19F I apparently have a huge deviation from the normal mean temperature. The average SD was .73, and even then, I am off by about .46. This could be due to my growing up in a colder climate in New York, or some medical conditions/medication. My data is very varied, which goes along with my lifestyle. I am never really doing the same thing twice, running around with different schedules each day, spending a lot of time outside, going back and forth because I forgot things at my dorm or such.
I was a lot cooler than Mara. Although it’s stated that the SD is .7, I was a full 1.06 degrees cooler. Then again, she exercises and is probably more active than I am. In addition, I am not very representative of the male population. I am more towards the introverted extreme, spending as much time as I can inside, in front of a keyboard.
97.06F – 32F * 5/9 =36.14 C
