1. Suppose you have the following dataset which contains the information of the students. You can use this dataset to solve the following questions.
Table 1: Sample Dataset: Heights, Weights, Test Scores, and Gender
| Gender | Height (cm) | Weight (kg) | Test Score |
| :--- | :--- | :--- | :--- |
| Male | 175 | 70 | 85 |
| Female | 163 | 55 | 78 |
| Male | 180 | 80 | 92 |
| Female | 155 | 45 | 70 |
| Male | 170 | 65 | 75 |
| Female | 168 | 58 | 80 |
| Male | 185 | 90 | 88 |
| Female | 160 | 50 | 72 |
| Male | 178 | 75 | 80 |
| Female | 162 | 52 | 10 |
| Male | 172 | 68 | 82 |
| Female | 170 | 60 | 85 |
| Male | 181 | 77 | 78 |
| Female | 165 | 48 | 74 |
| Male | 176 | 72 | 90 |
| your gender | your height | your weight | x |
where x is the last two digits of your id.
(i) Which types of variables are contained in the dataset, and what are the levels of measurements of these variables?
(ii) Create a frequency distribution table for the test scores in the dataset.
(iii) Visualize the frequency distribution of test scores using an appropriate graph.
(iv) Discuss any patterns or insights you observe in the distribution of test scores.
(v) Visualize the distribution of heights and weights separately for males and females using appropriate graphs (e.g., Pie chart, histograms, box plots). Analyze any differences in the distributions between genders.
(vi) Calculate the mean, median, and mode for both heights and weights separately. And calculate mean, median, and mode using frequency distribution. Compare these estimators with the estimators found for ungrouped data
(vii) Compare the central tendency measures (mean, median, mode) of heights and weights. Which measure is most appropriate for describing the "typical" height and weight in this dataset, and why?
(viii) Discuss any differences in central tendency measures between male and female participants for heights, weights, and test scores.
(ix) Calculate the range, variance, standard deviation, mean absolute deviation and coefficient of variation for both heights and weights separately.
(x) Interpret the results of each measure of dispersion for heights and weights. What do they indicate about the variability in heights and weights?
(xi) Define a threshold for outliers. Typically, outliers are considered to be observations that fall below Q1 - 1.5 * IQR or above Q3 + 1.5 * IQR. Identify any observations that fall outside the defined thresholds for outlier detection.
(xii) Discuss any limitations or biases present in the dataset and how they might affect the results of your analysis. Propose potential solutions or strategies to address these limitations and improve the validity of the analysis.
(xiii) Calculate the skewness and kurtosis of the variable test score and interpret your findings.
