1 line should divide the curve in half. Draw 3 lines to the right of this middle line, and 3 more to the left. These should divide each of the curve’s halves into 3 evenly spaced sections and one tiny section at the tip.
Suppose your data has a mean of 16 and a standard deviation of 2. Mark the center line with. 16. Add standard deviations to mark the first line to the right of the center with 18, the next to the right with 20, and the rightmost line with 22. Subtract standard deviations to mark the first line to the left of the center with 14, the next line to the left with 12, and the leftmost line with 10.
Each section immediately to the right and left of the center line will contain 34%, for a total of 68. The next sections to the right and left will each contain 13. 5%. Add these to the 68 percent to get 95% of your data. The next sections over on each side will each contain 2. 35% of your data. Add these to the 95 percent to get 99. 7% of your data. The remaining tiny left and right tips of the data each contain 0. 15% of the remaining data, for a total of 100%.
1 standard deviation above the mean would equal 4. 5 kg, and 1 standard deviation below equals 3. 5 kg. 2 standard deviations above the mean would equal 5 kg, and 2 standard deviations below would equal 3 kg. 3 standard deviations above the mean would equal kg, and 3 standard deviations below would equal 2. 5 kg.
Imagine you are asked to find the upper and lower weights for 68% of a population of cats. You would need to look at the two centermost sections, where 68% of data will fall. Similarly, imagine the mean weight is 4 kilograms, with a standard deviation of 0. 5 kilograms. If you are asked to find the proportion of cats above 5 kilograms, you need to look at the rightmost section (2 standard deviations away from the mean).
2 standard deviations above the mean will be 5 kilograms, and 1 standard deviation below the mean will be 3. 5 kilograms. This means that 81. 5% (68% + 13. 5%) of the cats weigh between 3. 5 and 5 kilograms.
The lowest 2. 5% of data would fall below 2 standard deviations from the mean. If the mean is 4 kilograms, and standard deviation is 0. 5, then the lowest 2. 5% of cats will weight 3 kilograms or less (4 - 0. 5 x 2).
