Basic statistics SLP3

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Student Name

Allied American University

Author Note

This paper was prepared for [INSERT COURSE NAME], [INSERT COURSE ASSIGNMENT] taught by [INSERT INSTRUCTOR’S NAME].

Continuing with the data collected below, write a paper (2- to 3-page, typed Word document) including all of the following content:

• Include the data from below.

Create a frequency distribution table for the data. You can use Excel or Word.

Calculate the standard deviation.

Calculate the variance.

Is this a normal distribution? How do you know? 

What are the implications? 

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.

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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 would be the probability distribution. As I already said, I try to sleep for 7 hours at 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.