Statistics SLP2 (See attachment)
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DG_SLP2.rtfMath 201 SLP 16
Math 201 SLP
Math 201 SLP
xxxxxxxxxxxx
University
Author Note
This paper was prepared for MATH 201, SLP , taught by xxxxxxxx
Using the data you collected in the last assignment (see below for last assignment), write a paper (2- to 3-page typed Word document) including all of the following content:
- Calculate the mean, median, and mode of your collected data. Show and explain your calculations.
Are these numbers higher or lower than you expected? Explain.
Which of these measures of central tendency do you think most accurately describes the variable you are looking at? Provide your justification.
Create a box plot to represent the data, labeling and numerating all 5 points on the box plot. For the plot, you may draw and insert it in your paper as a picture. Make sure it is legible.
The subject statistics is really interesting due to many facts. One of the facts which makes this interesting to me is, it collects the data or information from real life and tries to make a bridge between that data with events. We can get plenty of information from the data which can be used for better purpose like predicting the future.
Here there are lots of daily activities from where I can collect data for this project. I have chosen the daily sleeping time, as I thought that could be an interesting area to look into. The data collection process was quite easy. For data collection process I started my stopwatch when I went to my bed to sleep. And when I woke up I stopped it to check out how many minutes I slept. I considered minutes I slept rather than taking hours and considered the closest minute.
We know a person need around 7-8 hours of daily sleep to be healthy and active in regular life. I also try to follow that and try to sleep at least 7 hours or 420 minutes daily.
I have collected the data for 1 month (30 days) which is given below (This was easy for me to do because I track my sleeping hours anyway). The data below is shown in minutes not hours.
492
382
375
401
454
448
457
417
369
473
391
511
397
432
407
462
447
327
409
360
479
374
437
444
450
430
407
506
345
360
Here we can see that I collected the data for only one variable so no independent and dependent variables concept can be applied here.
However I can use the other techniques I learned here to analyze the data. The first thing would be the probability distribution. As I already stated, I try to sleep for 7 hours at the least, and due to random errors there is obviously some variation in the daily sleep time. Thus the theoretical distribution is normal. The experimental distribution is also expected to be normal as the data is collected for a large number of days. So we are quite sure about the probability distribution however we can also check it using a graph like histogram or a box plot. The obtained histogram and box plot of the data are given below.
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Sleeping Time
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Histogram of Sleeping Time
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Boxplot of Sleeping Time
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We can see that the histogram suggests a left skewed distribution but that largely depends on the class intervals we are taking. The box plot on the other hands shows no significant deviation from the symmetric distribution. So let’s check the measures of central tendency and variation to be sure. The obtained results are given below.
Descriptive Statistics: Sleeping Time
Variable
Mean
StDev
Variance
CoefVar
Minimum
Q1
Median
Q3
Maximum
Sleeping Time
421.43
47.98
2302.05
11.38
327.00
380.25
423.50
454.75
511.00
N for
Variable
Range
IQR
Mode
Mode
Skewness
Kurtosis
Sleeping Time
184.00
74.50
360,407
2
0.00
-0.70
The output suggests that the center of the distribution is near 422 as the mean and median is close to that value. The distribution is bimodal. The measures of variation like standard deviation, variance, range and Interquartile range suggests a low variation. We can also see that the skewness coefficient is 0 suggesting that the data is roughly symmetric around the mean. We can be also interested to know about the confidence interval of the mean. The obtained output is given below.
One-Sample T: Sleeping Time
Variable
N
Mean
StDev
SE Mean
95% CI
Sleeping Time
30
421.43
47.98
8.76
(403.52, 439.35)
From the above output we can see that the 95% confidence interval for the population mean sleeping time is (403.52, 439.35). So we can be 95% confident that the average sleeping time falls within 403 .52 minutes and 439.35 minutes.
