Bell Curve and Standard Deviation
The bell curve is literally, the symmetrical curve created on a graph when using a frequency distribution method for a set of data, splitting the mean symmetrically. There is a big difference between standard deviation and the bell curve! Standard deviation shows the difference in variation from the average; the bell curve, also normal distribution or Gaussian distribution, shows the standard deviation and is created by the normal or equal distribution of the mean among either half.
The bell curve is an important distribution pattern occurring in many different forms every day, all around us. Some example include: height, blood pressure, lengths of manufactured objects, etc… Most data creates a bell-shaped curve when graphed on a histogram (hints the name :). Bell curves have a single central peak at the mean of the data. Fifty percent of the distribution lies to the left of the mean and fifty percent lies to the right of the mean.
The distribution of the bell curve is controlled by the standard deviation (from that set of data). The smaller the standard deviation, the more concentrated the data in the bell curve will be. The bell curve/ normal distribution equation: At the Grauer Algebra 2 Corporation, the ages of all new employees hired during the last 5 years are normally distributed. Within this curve, 95. 4% of the ages, centered about the mean, are between 24. 6 and 37. 4 years. Find the mean age and the standard deviation of the data. | Solution: As was seen in Example 1, 95. 4% implies a span of 2 standard deviations from the mean. The mean age is symmetrically located between -2 standard deviations (24. 6) and +2 standard deviations (37. 4). The mean age is _24. 6 + 37. 4 = 31 years of age. 2 From 31 to 37. 4 (a distance of 6. 4 years) is 2 standard deviations. Therefore, 1 standard deviation is (6. 4)/2 = 3. 2 years. | | | |