IM3.7.6 Basics
Mean and Standard Deviation
What is the mean of a set of data? What is the standard deviation?[i][b]The mean is the average and the standard deviation measures how spread out the data is.[/b][/i]To calculate the standard deviation, [br]1. Find the mean, [br]2. Find the difference between each data point and the mean. These values are called deviations from the mean, and a deviation is denoted by .[br]3. Square each of the deviations.[br]4. Find the sum of the squared deviations.[br]5. Divide the sum of the squared deviations by .[br]6. Determine the square root. [br][br]Standard deviation in the real world is almost always found using calculators or other technology.
Distribution of Battery Life
Have you ever noticed how sometimes batteries seem to last a long time, and other times the batteries seem to last only a short time?The histogram above shows the distribution of battery life (hours) for a sample of batteries of the same brand. When studying a distribution, it is important to think about the [b]shape, center, and spread[/b] of the data.[br]1. Would you describe the distribution of battery life as approximately symmetric or as skewed? Explain your answer.[br][br]2. Is the mean of the battery life distribution closer to 95, 105, or 115 hours? Explain your answer.[br][br]3. Consider 5, 10, or 25 hours as an estimate of the standard deviation for the battery life distribution. a. Consider 5 hours as an estimate of the standard deviation. Is it a reasonable description of a typical distance from the mean? Explain your answer.[br][br]b. Consider 10 hours as an estimate of the standard deviation. Is it a reasonable description of a typical distance from the mean? Explain your answer.[br][br]c. Consider 25 hours as an estimate of the standard deviation. Is it a reasonable description of a typical distance from the mean? Explain your answer.