Final answer:
The shape of a distribution is typically described in terms of being uniform, exponential, normal, or skewed. The number of bars in a histogram affects its granularity and the ease with which one can determine its shape.
Step-by-step explanation:
The overall shape of a distribution can be described in several ways, including whether it has a uniform, exponential, or normal shape. The shape will be evident by drawing a smooth curve through the tops of the bars in a histogram. If the graph has a consistent height across all its bars, it would be described as having a uniform distribution. If the graph has a peak at one end and tapers off towards the other end, it might represent an exponential distribution. A bell-shaped curve that is symmetrical around the center would suggest a normal distribution.
Changing the number of bars in a histogram, which is also referred to as the number of bins, may affect the appearance of the distribution. If there are too few bins, important features and variations in the data may be obscured, resulting in an overly simplified representation of the distribution. Conversely, having too many bins might lead to a histogram that is overly complex, making it hard to identify the overall shape of the distribution due to too much granularity.
Regarding skewness, a distribution might be described as right skewed or positively skewed if it tails off to the right, while a left or negatively skewed distribution tails off to the left. A symmetrical distribution should have its mean, median, and mode all located at the center peak.
When analyzing plots such as box plots, histograms, or theoretical distributions in mathematical statistics, one is often comparing the actual data to a theoretical expectation. For example, in the context of the Central Limit Theorem (CLT), the distribution of sample means is expected to approximate a normal distribution, regardless of the shape of the population distribution from which samples are taken, given a sufficiently large sample size (n).