A unimodal distribution is a distribution that has one clear peak. A unimodal distribution can either be symmetrical or nonsymmetrical. A symmetrical distribution is one where the mean, mode, and the median are all equal. In such a distribution, the intervals of gains or losses exhibit the same frequency.

The shape of a distribution is described by its number of peaks and by its possession of symmetry, its tendency to skew, or its uniformity. (Distributions that are skewed have more points plotted on one side of the graph than on the other.) PEAKS: Graphs often display peaks, or local maximums.

How would you describe the shape of the histogram? Bell-shaped: A bell-shaped picture, shown below, usually presents a normal distribution. Bimodal: A bimodal shape, shown below, has two peaks. Skewed right: Some histograms will show a skewed distribution to the right, as shown below.

The standard normal distribution has two parameters: the mean and the standard deviation. Symmetrical distribution is one where a dividing line produces two mirror images, but the actual data could be two humps or a series of hills in addition to the bell curve that indicates a normal distribution.

What Is Symmetrical Distribution? A symmetrical distribution occurs when the values of variables appear at regular frequencies and often the mean, median, and mode all occur at the same point. If a line were drawn dissecting the middle of the graph, it would reveal two sides that mirror one other.

The uniform distribution is symmetric. The probabilities are exactly the same at each point, so the distribution is basically a straight line. An example of a uniform probability distribution could be picking a card from a deck: the probability of picking any one card is the same: 1/52.

A distribution is symmetrical if a vertical line can be drawn at some point in the histogram such that the shape to the left and the right of the vertical line are mirror images of each other. The mean, the median, and the mode are each seven for these data.

Which of the following distributions are always symmetrical? All continuous distributions are symmetrical.

The normal distribution is a symmetrical, bell-shaped distribution in which the mean, median and mode are all equal. It is a central component of inferential statistics. The standard normal distribution is a normal distribution represented in z scores. It always has a mean of zero and a standard deviation of one.

The normal distribution is the most important probability distribution in statistics because it fits many natural phenomena. For example, heights, blood pressure, measurement error, and IQ scores follow the normal distribution. It is also known as the Gaussian distribution and the bell curve.

All normal distributions are symmetric, unimodal, bell-shaped, and have their maximum at the mean=mode=median. All normal distributions are continuous and have asymptotic tails—never touching the x-axis. The standard normal distribution is sometimes called the unit normal distribution.