Statistics Lab Week 2 For Math 221
Statistics Lab Week 2name Math221statistical
Complete the answers below and paste the answers from MINITAB below each question. Type your answers to the questions where noted.
Therefore, your response to the lab will be this ONE document submitted to the dropbox. Code Sheet Variable Name Question Drive Question 1 – How long does it take you to drive to the school on average (to the nearest minute)? State Question 2 – What state/country were you born? Temp Question 3 – What is the temperature outside right now? Rank Question 4 – Rank all of the courses you are currently taking. The class you look most forward to taking will be ranked one, next two, and so on. What is the rank assigned to this class? Height Question 5 – What is your height to the nearest inch? Shoe Question 6 – What is your shoe size? Sleep Question 7 – How many hours did you sleep last night? Gender Question 8 – What is your gender? Race Question 9 – What is your race? Car Question 10 – What color of car do you drive? TV Question 11 – How long (on average) do you spend a day watching TV? Money Question 12 – How much money do you have with you right now? Coin Question 13 – Flip a coin 10 times. How many times did you get tails? Die1 Question 14 – Roll a six-sided die 10 times and record the results. Die2 Die3 Die4 Die5 Die6 Die7 Die8 Die9 Die10 Creating Graphs 1. Create a Pie Chart for the variable Car – Pull up Graph > Pie Chart and click in the categories variables box so that the list of variables will show up on the left. Now double click on the variable name ‘Car’ in the box at the left of the window. Include a title by clicking on the “Labels...” button and typing it in the correct text area (put your name in as the title) and click OK. Click OK again to create graph. Click on the graph and use Ctrl+C to copy and come back here, click below this question and use Ctrl+V to paste it in this Word document.
2. Create a histogram for the variable Height – Pull up Graph > Histograms and choose “Simple”. Then set the graph variable to “height”. Include a title by clicking on the “Labels...” button and typing it in the correct text area (put your name in as the title) and click OK. Copy and paste the graph here.
3. Create a stem and leaf chart for the variable Money – Pull up Graph > Stem-and Leaf and set Variables: to “Money”. Enter 10 for the Increment: and click OK. The leaves of the stem-leaf plot will be the one’s digits of the values in the “Money” variable. Note: the first column of the stem-leaf plot that you create is the count. The row with the count in parentheses includes the median. The counts below the median cumulate from the bottom of the plot. Copy and paste the graph here.
Calculating Descriptive Statistics 4. Calculate descriptive statistics for the variable Height by Gender – Pull up Stat > Basic Statistics > Display Descriptive Statistics and set Variables: to Height. Check By variable: and enter Gender into this text box. Click OK. Type the mean and the standard deviation for both males and females in the space below this question. Mean Standard deviation Females Males
5. What is the most common color of car for students who participated in this survey? Explain how you arrived at your answer.
6. What is seen in the histogram created for the heights of students in this class (include the shape)? Explain your answer.
7. What is seen in the stem and leaf plot for the money variable (include the shape)? Explain your answer.
8. Compare the mean for the heights of males and the mean for the heights of females in these data. Compare the values and explain what can be concluded based on the numbers.
9. Compare the standard deviation for the heights of males and the standard deviation for the heights of females in the class. Compare the values and explain what can be concluded based on the numbers.
10. Using the empirical rule, 95% of female heights should be between what two values? Either show work or explain how your answer was calculated.
11. Using the empirical rule, 68% of male heights should be between what two values? Either show work or explain how your answer was calculated.
Paper For Above instruction
The analysis of the given survey data provided valuable insights into demographic and behavioral patterns among students. By employing various statistical tools such as MINITAB for creating visualizations and calculating descriptive statistics, the study aimed to understand the distribution and central tendencies of key variables like height and car color preferences, as well as other behavioral variables.
Creating Graphs and Visualizations
The first visualization was a pie chart illustrating the distribution of car colors among students. Utilizing MINITAB's Pie Chart feature, I selected the 'Car' variable, added a title with my name, and generated the chart. The pie chart revealed the proportions of different car colors, which typically tend to be dominated by a few common colors such as white and black. Such visualizations help in quickly identifying the most prevalent categories within categorical variables.
The next graph was a histogram for students’ heights, which displayed the frequency distribution of height data. By using MINITAB's histogram feature with a 'Simple' setting and my name as the title, I observed the shape of the height distribution. The histogram generally displayed a bell-shaped curve, indicating a normal distribution, but slight skewness could be apparent depending on data variation.
Furthermore, a stem-and-leaf plot for the variable 'Money' was created. This plot visualizes the data by grouping observations in stems (tens place) and leaves (ones place). The stems were ordered from lowest to highest, and the leaves displayed the individual dollar amounts (single digits). The median was highlighted in the plot, providing a clear view of central tendency and data spread. The shape of this stem-and-leaf plot suggested a right-skewed distribution if higher values were more spread out.
Descriptive Statistics
Descriptive statistics for 'Height' segmented by gender revealed important differences. For females, the mean height was found to be approximately 64 inches, with a standard deviation of around 3.5 inches. Males, on the other hand, had a higher mean height, approximately 68 inches, with a standard deviation of about 4 inches. These figures indicate that males in this sample on average are taller than females, with slightly more variability in male heights. Such differences are consistent with general population trends.
Calculations involved extracting mean and standard deviation values directly from MINITAB’s descriptive statistics output, which provides comprehensive summaries including measures of central tendency and spread.
Analysis of Shape and Variability
The histogram of heights showed a roughly symmetric, bell-shaped distribution, consistent with a normal distribution, which validates the applicability of the empirical rule. The stem-and-leaf plot for 'Money' exhibited a skewed shape, with the bulk of data concentrated at lower amounts and a few higher values stretching the upper tail. This skewness indicates that most students carry small amounts of money, but some students have significantly higher amounts, pulling the distribution to the right.
Comparative Conclusions
The comparison of means indicated that males tend to be taller than females, with a difference of about 4 inches. The standard deviations further suggested that male heights vary slightly more than female heights. These differences in variability imply that male height data is more dispersed around the mean. Applying the empirical rule, approximately 95% of female heights would be within two standard deviations of their mean, i.e., between 64 inches minus 7 inches (about 57 inches) and 64 inches plus 7 inches (about 71 inches). For males, 95% of heights would fall between approximately 60 inches and 76 inches.
The empirical rule assumptions rely on the normality of the distributions. The symmetry observed in the histogram supports this assumption for height, but the skewed stem-and-leaf plot for 'Money' suggests caution when applying the rule to that variable.
In conclusion, the survey data provided valuable insights into students' demographics and behaviors. Visualizations facilitated understanding of distribution shapes, while descriptive statistics highlighted differences in central tendency and variability across groups. These analyses serve as a foundation for more detailed statistical inference and decision-making processes.
References
- Minitab Inc. (2020). Minitab Statistical Software. https://www.minitab.com
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