1. **Problem Statement:** We have 120 BMI data values from a survey. We need to: - Order the data ascendingly. - Create a grouped frequency distribution. - Draw histograms and cumulative frequency graphs. - Calculate mean, median, variance, standard deviation, and coefficient of variation. 2. **Ordering the Data:** Sort all 120 BMI values from smallest to largest to form an ordered array. 3. **Grouped Frequency Distribution:** - Determine the range: max BMI - min BMI. - Choose class intervals (bins) that cover the range, e.g., intervals of width 5 or 2. - Count how many BMI values fall into each interval. 4. **Histogram:** - Plot intervals on the x-axis. - Plot frequencies on the y-axis. - Draw bars for each interval with height equal to frequency. 5. **Cumulative Relative Frequency Table:** - Calculate relative frequency for each class: frequency / total data count. - Calculate cumulative relative frequency by summing relative frequencies up to each class. 6. **Graphs from Cumulative Relative Frequency:** - i. Cumulative frequency curve: plot cumulative frequencies against upper class boundaries and connect smoothly. - ii. Cumulative frequency polygon: plot points at upper class boundaries with cumulative frequencies and connect with straight lines. - iii. Pie chart: sectors proportional to frequencies of each class. - iv. Cumulative relative frequency histogram: bars representing cumulative relative frequencies. 7. **Calculations:** - Mean: $$\bar{x} = \frac{\sum x_i}{n}$$ where $x_i$ are BMI values, $n=120$. - Median: middle value in ordered data or average of 60th and 61st values. - Variance: $$s^2 = \frac{\sum (x_i - \bar{x})^2}{n-1}$$ - Standard deviation: $$s = \sqrt{s^2}$$ - Coefficient of variation: $$CV = \frac{s}{\bar{x}} \times 100\%$$ 8. **Summary:** - Order data. - Create frequency table. - Draw histogram and cumulative graphs. - Calculate mean, median, variance, standard deviation, and CV. Due to the large data set, calculations and plots are best done using statistical software or spreadsheet tools for accuracy.