Statistics

Statistics
Homework 1
Name _____________________________________
There are two data files in the HW1 Folder, one is in SPSS form and it is: QLDiab.sav and the other is the same data file in Excel format: QLDiab.xlsx if you want to use a program other than SPSS. The data in these files is for a measure of Quality of Life of subjects with Type Ii diabetes. It has three variables: the QoL measure, time having diabetes as a category, and gender.
This data set will be used for both HW1 and HW2.
For HW1 to focus will be on graphics and for HW2 the focus will be on numerics. You will need to cut and past output into this form.
Let’s look at parts of the data file variable view:

1. Does it appear the Measure label is correct? Why do you feel this way?
The label is correct. That is because it offers a brief description of the variable of interest. In this case, the variable is the time that patients have spent since being diagnosed with diabetes.
2. Conduct frequency distribution and bar graph for the Gender variable.
Post the Frequency Distribution for Gender here:
Gender Count (f) Subtotal
Male 79 79
Female 121 200
Total 200 Post the Bar Graph for Gender here:

Complete this table:
Gender f %
Male 121 60.5
Female 79 39.5
3. Conduct frequency distribution and histogram for the Time category.
Post the frequency distribution here:
Time category Count (f) Subtotal
Less than 5 years 26 26
5 to 10 years 38 64
More than 10 years 136 200
Total 200 Post the histogram here:

Complete this table:
Time having Diabetes f % CfC%
Less than 5 years 26 13 26 13
5 to 10 years 38 19 64 32
More than 1 years 136 68 200 100
4. For the Quality of Life Measure:
Post a stem and leaf plot here:
Stem Leaf
0 9
1 0 0 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9
2 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 8 8 8 8 9 9 9 9 9
3 0 0 1 1 1 1 2 2 3 5 6
Complete the following table:
Quality of Life Score f % CfC%
8-9 1 0.5 1 0.5
10-11 6 3 7 3.5
12-13 22 11 29 14.5
14-15 35 17.5 64 32
16-17 16 8 80 40
18-19 29 14.5 109 54.5
20-21 18 9 127 63.5
22-23 17 8.5 144 72
24-25 19 9.5 163 81.5
26-27 17 8.5 180 90
28-29 9 4.5 189 94.5
30-31 6 3 195 97.5
32-33 3 1.5 198 99
34-35 1 0.5 199 99.5
36-37 1 0.5 200 100
Post a histogram here with a normal distribution included:

Post a boxplot here:

Are there any outliers? Yes, there are outliers. That is because there are values that are larger than the Q3 by 9 which is the interquartile range.
About what would be the value for the median? 19
About what would be the value of Q1? 15
About what would be the value of Q3? 24
5. Post a boxplot of the Quality of Life Score by Time variable:

Which group has the highest Quality of Life Score? Those who have had diabetes for less than 5 years
Which group has the lowest Quality of Life Score? Those who have had diabetes for more than 10 years
Discuss the outliers for the groups that have them:
Two groups have outliers. These are the 5 to 10 years group and the more than 10 years group. These is evidenced by the outlier values exceeding the difference between Q1 and Q3.
Homework 2
Name: _____________________
Use the same data used for homework 1 (QLDiab.sav or QLDiab.xlsx) and output generated for HW 1.
Determine the summary statistics for the three variables in the data file.
Here are the options for statistics you should pick:

Post the output table for the summary statistics for the three variables here:
Statistics
Quality of Life Score Time having DiabGender
N Valid 200 200 200
Missing 0 0 0
Mean 19.61 2.55 1.40
Std. Error of Mean .409 .051 .035
Median 19.00 3.00 1.00
Mode 14 3 1
Std. Deviation 5.785 .714 .490
Variance 33.466 .510 .240
Skewness.480 -1.265 .433
Std. Error of Skewness.172 .172 .172
Kurtosis -.568 .122 -1.831
Std. Error of Kurtosis .342 .342 .342
Range 27 2 1
Minimum 9 1 1
Maximum 36 3 2
Sum 3923 510 279
1. For the gender variable, what is the appropriate measure of central tendency and what is the value for it?
The mode is appropriate. This identifies males as the most common gender with a frequency of 121 while the females are the less common gender with a frequency of 79.
2. For the time variable, what are the two appropriate measures of central tendency and what are the values?
For the time variable, the two appropriate measures of central tendency are mode and median. Both the mode and median have been identified as ‘more than 10 years’ since the calculated value is 3 and this represents ‘more than 10 years’ label.
3. For the Quality of Life variable, what are the appropriate measures of central tendency and what are the values?
For the quality of life variable, the appropriate measures of central tendency are the mean (19.61), median (19), and mode (14).
4. Answer the following for the Quality of Life variable:
a. Define the mean and provide the value of the mean. It is the average for the figures and has been calculated as 19.61
b. Define the median and provide the value of the median. The median is the value that appears at the center when all the values are arranged in either an ascending or descending order. The median is 19
c. What is the value of the skewness coefficient and what does it say about the skewness of the distribution? The value is 0.480 and it indicates a positively skewed distribution.
d. How does the comparative relationship of the mean and median relate to the skewness coefficient? A large difference between mean and median values will result in a large skewness coefficient whereas a small difference between mean and median values will result in a large skewness coefficient.
e. It what way does the histogram found in HW1 confirm the skewness? The histogram confirms the skewness by showing that the distribution is asymmetric and most of the peaks are found towards the left side of the graph.
f. What does the kurtosis coefficient tell about the peakedness of the distribution? The kurtosis coefficient is -0.568. The negative value shows that the distribution graph has very light tails when compared to the normal distribution with uniform peaks across the different data points.
g Define the variance and provide the value for it. Variance is the quantification of the data spread and presented as the squared differences from the mean. It has been calculated as 33.466
h. Define the standard deviation and provide the value for it. Standard deviation is a measure of how far the values are spread from the mean. It has been calculated as 5.785
i. Verify the relationship between variance and standard deviation. The standard deviation is the square root of the variance to imply that the reverse calculation is true with the variance being the standard deviation squared. The standard deviation was calculated as 5.785 and its square is 33.466225 which is equivalent to the value calculated for the variance as 33.466 (3dp).
j. Add and subtract 3 times the standard deviation from the mean and provide those values. Discuss why these values are reasonably expected. The standard deviation is 5.785 while the mean is 19.61. 3-times the standard deviation is 17.355. Adding this value to the mean presents 36.965 while subtracting it from the mean presents 2.255. The range between 2.255 and 36.965 accounts for 99.7% of all the dataset. This follows the 68-95-99.7 rule where 1 standard deviation for the mean accounts for 68% of the data, 2 standard deviation from the mean accounts for 95% of the data while 3 standard deviation from the mean accounts for 99.7% of the data.