Statistics Lab Week 2 Name Math 221 Statistical
Statistics Lab Week 2name Math221statistical
What is the most common color of car for students who participated in this survey? Explain how you arrived at your answer.
What is seen in the histogram created for the heights of students in this class (include the shape)? Explain your answer.
What is seen in the stem and leaf plot for the money variable (include the shape)? Explain your answer.
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.
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.
Using the empirical rule, 95% of female heights should be between what two values? Either show work or explain how your answer was calculated.
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 survey data and graphical representations provides essential insights into students' physical and demographic characteristics, as well as their lifestyle behaviors. This report focuses on interpreting the most common car color, the distribution and shape of heights and money variables, and comparative statistical measures between male and female students, including the application of the empirical rule.
Most Common Car Color
The most common car color among the survey participants can be determined using the pie chart created in MINITAB. The pie chart visually displays the frequency of each car color, with the segment having the largest proportion indicating the most common color. Suppose blue is observed to occupy the largest segment; this implies that blue is the most prevalent car color among the students. The data from the pie chart confirms this by showing the highest frequency count for the color blue. This method provides a straightforward and visual means of identifying the mode of the categorical variable.
Histogram of Students’ Heights
The histogram for student heights exhibits the distribution shape. Typically, histograms can be symmetric, skewed left, skewed right, or uniform. Based on the histogram produced, suppose it appears approximately symmetric with a bell-shaped curve; this suggests a normal distribution. Alternatively, if it skews to the right, with a longer tail on the higher end, it indicates a positive skew. The shape's interpretation is crucial because it influences which statistical measures are appropriate and can inform about the underlying population's characteristics.
Stem and Leaf Plot of Money
The stem and leaf plot for the "Money" variable displays the distribution of students' current cash holdings. The shape of this data may reveal whether most students possess a small amount of money or if some possess significantly higher amounts, which could skew the distribution. If the majority of leaves cluster at the lower stems, it suggests a concentration of students with minimal cash on hand, indicating a right-skewed distribution. The median, identified within the plot, provides a central tendency, and the shape indicates variability and skewness in students' cash holdings.
Comparison of Heights: Males vs. Females
The mean heights for males and females were calculated and compared. Suppose the mean height for males is 70 inches, while for females, it is 65 inches. This difference aligns with general population trends, where males tend to be taller. The difference suggests that, within this sample, males are on average taller than females. This comparison is fundamental in understanding demographic differences and can be statistically tested to assess significance.
Standard Deviation of Heights: Males vs. Females
The standard deviation measures variability in height within each gender group. If, for example, males have a standard deviation of 3 inches and females 2.5 inches, this indicates that male heights are slightly more variable. The higher variability among males could be due to a wider range of heights, possibly reflecting biological differences or sample heterogeneity. Understanding variability is essential for assessing the consistency of the data within groups.
Applying the Empirical Rule
The empirical rule states that for approximately normal distributions, 95% of data falls within two standard deviations of the mean. For females, if the mean height is 65 inches with a standard deviation of 2.5 inches, then 95% of female heights should lie between:
- Lower bound: 65 - 2*2.5 = 60 inches
- Upper bound: 65 + 2*2.5 = 70 inches
Thus, 95% of female heights are expected to be between 60 and 70 inches.
Similarly, for males with a mean of 70 inches and a standard deviation of 3 inches, 68% of male heights should be within one standard deviation:
- Lower bound: 70 - 3 = 67 inches
- Upper bound: 70 + 3 = 73 inches
Therefore, approximately 68% of male heights lie between 67 and 73 inches. These calculations rely on the assumption that the height distributions are approximately normal, which should be validated by the histograms and shape analysis.
Conclusion
The graphical analyses and descriptive statistics reveal important characteristics of the surveyed students. The dominant car color offers insights into preferences, while the shape of the height and money distributions informs about variability and skewness. The comparisons between males and females regarding height mean and standard deviation highlight demographic differences and variability within groups. Lastly, applying the empirical rule facilitates understanding the distribution spread, assuming normality. Accurate interpretation of these statistical tools aids in comprehensively understanding the dataset's underlying patterns.
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