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Created: Jun 11, 2018
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M3A2: Group Project Report
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     My group and I created a small survey camparing age and exercise habits. We polled Facebook acquaintances and email contacts and collected a non-random sample of data. Respondents consisted of a convenience sampling of population. They were assured of the privacy of their identification and information and voluntarily answered the survey questions; answering the questions was presumed as consent on the part of the respondents. The following report depicts the data analysis of our survey.

We asked our respondents the following questions:

1. What is your age now?

2. How many minutes do you usually exercise at once?

3. Do you find that exercise difficulty increases with age?

 Select one: Yes or No

 4. How often do you exercise for 30 minutes or more per day?

 A) 5-7 times per week
B) 2-4 times per week
C) 3-5 times per month
D) 1-2 times per month
E) Rarely or never

Looking at a Categorical Variable

Responses of the question "How often do you exercise for 30 minutes or more per day?" are depicted in the pie chart below:

Result 1: Pie Chart of Exercise Frequency   [Info]
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Clearly, 2-4 times a week is the most prevalent answer from our respondents representing 37.59% of the sampled population. 5-7 times per week was surprisingly prevalent with 21.99%. The results of the remaining answers were very similar at 12.77%, 14.18%, and 13.48% respectively.

In order to see if the 'frequency of exercising 30 minutes or more' responses differ according to increased difficulty of exercising with age, we can consult the following bar plot:

Result 2: Bar Plot Harder with Age / Frequency   [Info]
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Exercising 2-4 times per week is prevalent in both groups, but markedly moreso in the group that admits to increased difficulty of exercising with age. Predictively, more respondents find that exercising increases in difficulty with age. The respondents that deny increased difficulty exercising with age surprisingly do not exercise very frequently; most exercise 5 times per month or less.

Looking at a Numerical Variable 

Responses to the question, "What is your age now?" are depicted in the histogram, boxplot, and summary statistics below:

Result 3: Histogram of Age   [Info]
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Result 4: Boxplot of Ages   [Info]
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Result 5: Summary Stats Exercise Survey   [Info]
Summary statistics:
ColumnnMeanVarianceStd. dev.MedianRangeMinMaxQ1Q3IQR



The histogram shown is skewed right, which is common when the mean value of the data is greater than the median. The median, which is generally unaffected by outliers, is 40 and the mean which can be greatly affected by outliers is 44 (rounded to the nearest whole number).


 The range of the data is 64. The range rule-of-thumb (range/4) in this data set computes to 16 which is in discrepancy with the standard deviation of 12.7. The Skewness of the data set and the presence of the outliers makes the range rule-of-thumb overestimate the standard deviation by 3.3.


The IQR of the data is 20 which is equal to the range of the middle half of the data. The lower value of the IQR is 34 and the upper value is 54.


The boxplot reveals an outlier of 85 which is a legitimate value and reasonable; many 85-year-old people are well able to participate in exercise activity. I do not consider this value to be erroneous.

Looking for a Relationship between Two Numerical Variables

Result 6: Scatter Plot Age / Minutes Exercising   [Info]
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The scatter plot shows a negative, widely scattered, and non-linear correlation between age and minutes exercised. Outliers of 120 minutes and 85 years of age are easily identifiable in the scatter plot.


Result 7: Correlation of Age and Minutes Exercised   [Info]
Correlation between Age and Minutes is:

While normal correlation coefficients are within a range of -1 to 1 and a value close to or equal to 0 depicts little to no correlation respectively, we can deduce that the correlation coefficient of 0.165 (from correlation critical values chart supplied) shows insignificant statistical correlation between age and minutes exercised.

Data set 1. Statistics Group Survey   [Info]
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