bell curve

Examples of bell curve in the following topics:

• Graphing the Normal Distribution

  • The graph of a normal distribution is a bell curve, as shown below.
  • Bell curve visualizing a normal distribution with a relatively large standard deviation.
  • The graph of a normal distribution is known as a bell curve.
  • Bell curve visualizing a normal distribution with a relatively small standard deviation.
  • Evaluate a bell curve in order to picture the value of the standard deviation in a distribution

• Introduction

  • Its graph is bell-shaped.
  • You see the bell curve in almost all disciplines.

• Assessing an Organization's Technological Needs

  • As successive groups of consumers adopt new technology a bell curve emerges - this is referred to as the innovation adoption life cycle (the blue bell curve on the above graphic).

• The Average and the Histogram

  • When a histogram is constructed on values that are normally distributed, the shape of columns form a symmetrical bell shape.
  • This is why this distribution is also known as a "normal curve" or "bell curve. " is an example of a normal distribution:
  • If represented as a 'normal curve' (or bell curve) the graph would take the following shape (where $\mu$ is the mean and $\sigma$ is the standard deviation):
  • A key feature of the normal distribution is that the mode, median and mean are the same and are together in the center of the curve.
  • A key feature of the skewed distribution is that the mean and median have different values and do not all lie at the center of the curve.

• Introduction to normal distribution

  • The symmetric, unimodal, bell curve is ubiquitous throughout statistics.
  • Indeed it is so common, that people often know it as the normal curve or normal distribution, shown in Figure 3.1.

• IQ Tests

  • Scores on IQ tests tend to form a bell curve with a normal distribution.
  • It is a statistical law that under a normal curve, 68% of scores will lie between -1 and +1 standard deviation, 95% of scores will lie between -2 and +2 standard deviations, and >99% percent of scores will fall between -3 and +3 standard deviations.
  • In a normally distributed bell curve, half the scores are above the mean and half are below.
  • IQ test scores tend to form a bell curve, with approximately 95% of the population scoring between two standard deviations of the mean score of 100.

• Normal distribution model

  • The normal distribution model always describes a symmetric, unimodal, bell-shaped curve.
  • However, these curves can look different depending on the details of the model.
  • As you can probably guess, changing the mean shifts the bell curve to the left or right, while changing the standard deviation stretches or constricts the curve.
  • Both curves represent the normal distribution, however, they differ in their center and spread.

• Introduction to Normal Distributions

  • It is sometimes called the "bell curve," although the tonal qualities of such a bell would be less than pleasing.
  • It is also called the "Gaussian curve" after the mathematician Karl Friedrich Gauss.

• Optional Collaborative Classrom Activity

  • Then draw a smooth curve through each histogram.
  • Is each curve somewhat bell-shaped?
  • Do you think that if you had recorded 200 data values for men and 200 for women that the curves would look bell-shaped?
  • The curve is symmetrical about a vertical line drawn through the mean, µ.
  • Since the area under the curve must equal one, a change in the standard deviation, σ, causes a change in the shape of the curve; the curve becomes fatter or skinnier depending on σ.

• Probability Histograms and the Normal Curve

  • Many different types of distributions can be approximated by the normal curve.
  • If you were to construct a probability histogram of these events with many trials, the histogram would appear to be bell-shaped.
  • If the graph is approximately bell-shaped and symmetric about the mean, you can usually assume normality.
  • Notice that the histogram is not bell-shaped, indicating that the distribution is not normal.
  • The histogram looks somewhat bell-shaped, indicating normality.