Stem And Leaf Of Money 20 Leaf Unit

Stem And Leaf Of Moneyn 20leaf Unit 1090124456667312498212853033

Analyze the stem-and-leaf plot for the money variable, describe its shape, examine the histogram of student heights and its shape, compare the mean and standard deviation of male and female heights, and apply the empirical rule to determine the ranges within which most female and male heights fall.

Paper For Above instruction

The provided data involves several statistical analyses of a sample of students, focusing on monetary values, heights, and gender-based height differences. The initial step involves examining the stem-and-leaf plot for the money variable. The plot indicates a distribution where values cluster in certain ranges, offering insight into the data's shape. Visual inspection of this plot suggests whether the distribution is symmetric, skewed, or uniform. Given the shape, one can determine if the data is normally distributed or exhibits skewness.

Likewise, the histogram depicting students' heights provides a visual representation of the data's distribution. The shape—whether bell-shaped, skewed, uniform, or bimodal—offers crucial information about the nature of variability within the heights. For example, a bell-shaped histogram indicates a normal distribution, which is often assumed in many statistical analyses.

Comparing the mean heights for males and females reveals differences in average stature. The mean height of males (69.78 inches) exceeds that of females (67.27 inches), suggesting that, on average, males are taller than females within this sample. The standard deviations (2.533 inches for females and 4.21 inches for males) indicate the variability of heights within each gender group. A higher standard deviation among males suggests greater variability in male heights compared to females, implying that female heights are more tightly clustered around the mean.

Using the empirical rule, which states that approximately 95% of data values lie within two standard deviations of the mean for a normal distribution, we can estimate the ranges of most heights. For females, with a mean of 67.27 inches and a standard deviation of 2.533 inches, 95% of heights are expected to fall between:

67.27 - 2(2.533) = 67.27 - 5.066 = 62.204 inches

and

67.27 + 2(2.533) = 67.27 + 5.066 = 72.336 inches

Similarly, for males, with a mean of 69.78 inches and a standard deviation of 4.21 inches, 95% of heights should be between:

69.78 - 2(4.21) = 69.78 - 8.42 = 61.36 inches

and

69.78 + 2(4.21) = 69.78 + 8.42 = 78.20 inches

This analysis suggests that the majority of female heights are between approximately 62.2 and 72.3 inches, while male heights predominantly range from about 61.4 to 78.2 inches, aligning with typical expectations of height distribution in these gender groups.

References

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