Analyzing Sleep Habits: Data Graphing & Numerical Summaries

Lilyhan Liao Yaxin Fang Lab 2: Graphing Data and Numerical Summaries Two hundred fifty college students in Indiana participated in a study examining the associations among sleep habits, sleep quality and physical/emotional factors. Participants completed an online survey about sleep habits that included the Pittsburgh Sleep Quality Index (PSQI), the Epworth Sleepiness Scale (ESS), the Horne-Ostberg Morningness Eveningness Scale (MES), the Subjective Units of Distress Scale (SUDS), and questions about academic performance and physical health. 1. (2 points) Fill in the chart below. In the second column, record whether the variable is quantitative or categorical, based on the data in the lab dataset. In the third column record whether a bar graph or a histogram correctly shows the distribution of the data. Variable Name Type of Variable Type of Graph Sleep time week Numerical Histogram Gender Categorical Bar Graph Weight Numerical Histogram Class Categorical Bar Graph Age Numerical Histogram 2. (2 points) Use SPSS to make a bar graph for the variable Gender. Copy and paste the graph into this document here.

3. (2 points) Use SPSS to make a histogram for the variable Sleep_time_week. Copy and paste the graph into this document here. 4. (2 points) Use SPSS to find the mean and standard deviation of Sleep_time_week. Record the values rounded to two decimal places below. Copy and paste the SPSS output into this document here. Descriptives

Statistic Std. Error Sleep Time During the Week Mean 6.9966 .04222 95% Confidence Interval for Mean Lower Bound 6.9132 Upper Bound 7.0800 5% Trimmed Mean 6.9977 Median 6.9700 Variance .267 Std. Deviation .51708 Minimum 5.67 Maximum 8.31 Range 2.64 Interquartile Range .62 Skewness .032 .198 Kurtosis .031 .394 Sleep_time_week: Mean: ~7.00 Standard deviation: ~.51708 5. (4 points) SPSS is not used in this course to find quartiles because the program’s default method yields an unbiased estimate of the population quartiles. Rather, in this course, the interest is to find quartiles associated with the sample. BY HAND, find the 5-number summary of Sleep_time_week. Show your work on how to find the location of Q1, Median and Q3. (You can use SPSS to sort the data from smallest to largest first and use the row number on the left of the Data View tab to make the job easier). 5.67, 5.67, 5.76, 5.94, 6.03, 6.04, 6.04, 6.16, 6.26, 6.27, 6.27, 6.3, 6.36, 6.36, 6.37, 6.39, 6.4, 6.42, 6.42, 6.43, 6.43, 6.43, 6.45, 6.45, 6.45, 6.46, 6.54, 6.55, 6.56, 6.58, 6.6, 6.6, 6.63, 6.64, 6.64, 6.67, 6.67, 6.68, 6.68, 6.69, 6.69, 6.69, 6.7, 6.73, 6.73, 6.73, 6.75, 6.76, 6.78, 6.79, 6.8, 6.81, 6.82, 6.82, 6.83, 6.83, 6.85, 6.86, 6.87, 6.88, 6.89, 6.89, 6.89, 6.89, 6.9, 6.93, 6.93, 6.94, 6.94, 6.95, 6.95, 6.96, 6.96, 6.97, 6.97, 6.97, 6.98, 6.99, 6.99, 6.99, 6.99, 7.04, 7.04, 7.05, 7.07, 7.07, 7.07, 7.07, 7.08, 7.08, 7.08, 7.09, 7.12, 7.12, 7.13, 7.14, 7.15, 7.16, 7.17, 7.17, 7.18, 7.19, 7.2, 7.21, 7.23, 7.24, 7.24, 7.25, 7.26, 7.26, 7.28, 7.29, 7.29, 7.3, 7.31, 7.31, 7.33, 7.37, 7.43,

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7.45, 7.45, 7.51, 7.52, 7.52, 7.53, 7.53, 7.53, 7.57, 7.58, 7.58, 7.59, 7.6, 7.6, 7.63, 7.66, 7.75, 7.75, 7.77, 7.79, 7.8, 7.81, 7.84, 7.88, 7.95, 8.02, 8.05, 8.06, 8.1, 8.14, 8.31 Min Q1 Median Q3 Max 5.67 6.68. 6.97. 7.29 8.31 5# summary for Sleep_time_week: 6. (2 points) Inspect the histogram for the variable Sleep_time_week created in Question 3. Is the graph approximately symmetric, skewed left, or skewed right? Explain how the graph’s shape is related to the Mean and Median calculated in Questions 4 and 5. The graph is approximately symmetric. The histogram has a prominent peak in the center and similar tapering on the left and the right as if they mirror each other. This tells us that both the mean and median can be found in the center of the graph. The mean and median should be close in value. Median = Mean 6.97 is close to 7.00. 7. (2 points) BY HAND, use the 1.5*IQR Rule to determine if there are any suspected outliers for the variable Sleep_time_week. Show your work. State and explain why there are or are not suspected outliers. If there are suspected outliers, identify the values. To find the Upper Bound: Q3+ IQR*1.5 To find the Lower Bound: Q1- IQR*1.5 IQR: Q3-Q1 IQR: 7.29-6.68= 0.61 High Outlier >Q3+ IQR*1.5 Low Outlier < Q1-IQR*1.5 Upper Bound: 7.29+ 1.5(0.61) = 8.205 Lower Bound: 6.68- 1.5(0.61) = 5.765 High Outlier: 8.31> 8.205 Low Outliers: 5.67< 5.765, 5.67<5.767, 5.76<5.765 There is one high outlier and three low outliers. 8. (2 points) Use SPSS to make a boxplot or modified boxplot for the variable Sleep_time_week. Copy and paste the graph into this document here. In the space below, explain where the numbers calculated in Question 5 appear.

The min, max, Q1, median, and Q3 values that I found all show up on this box plot. The min sits right below 6 as the bottom whisker. The max sits right above 8 as the top whisker. Q1 sits between 6.50 and 7.00 and starts the beginning of the box. Q2 or in other words the median sits right below 7.00 and is the belt(middle) of the box. Q3 sits right between 7.00 and 7.50 and is the end of the box. 9. (2 points) For the variable Sleep_time_week, explain if the mean and standard deviation are appropriate to describe the distribution. If not, what should be used instead? Mean and standard deviation would be appropriate for this distribution because it's symmetrical. Because the data is not significantly skewed, mean and standard deviation would be able to accurately measure the center and the overall spread.

Lab 2 (1)

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