If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

## AP®︎/College Statistics

### Course: AP®︎/College Statistics>Unit 2

Lesson 3: Describing the distribution of a quantitative variable

# Classifying shapes of distributions

When we describe shapes of distributions, we commonly use words like symmetric, left-skewed, right-skewed, bimodal, and uniform. Not every distribution fits one of these descriptions, but they are still a useful way to summarize the overall shape of many distributions.

## Want to join the conversation?

• i mean do people mesure house flies?
• What are some applications of this? Never seen it used in real life? @ do baseball statisticians use this?
• you could use this in real life because it can tell you correlation and averages, like on the coffee graph you can look and see most people drink 3 cups a day. Another example is how you can see that in almost all skewed distribution you see correlation (ex. in left tailed as x goes up y goes up) so you use this in real life to be able to see things like how exercising every day relates to longer life span. Though while doing math memorizing distribution types can help with just being able to glance at the graph and getting the gist. (ps. I don't know much about baseball so wouldn't know if base ball statisticians use this but I would guess they do because almost all statisticians do.)
• Is a random distribution always uniform? What about the viceversa?

The first implication (random=>uniform) seems reasonable: if you toss a coin you expect a uniform distribution of tails and heads as the number of throws grows bigger and bigger, the same reasoning seems to apply for throwing dice or generating random numbers.

The second implication (uniform =>random) "feels" false but I can't come up with a meaningful counter example. Any ideas?
• If graphed, a uniform distribution will look like what most people would describe as a "bell-shaped" curve, with the majority of the data points clustering around the central tendencies, like test scores. There will be a lot of people in a class that get a passing grade, while a small portion will not get a passing grade, and a small portion will get above passing grade. Meanwhile, a random distribution, if graphed, will look uniform. Because it is random, then any given data point will have an equal chance of landing in each bucket. For example, rolling the dice will yield a roughly uniform distribution graph because each time you roll the die, each number is equally likely to come up. But if you randomly survey a person's test scores, the probability that he or she getting a average, above-average, or below-average score will not be equivalent. That student will be much more likely to get a "C" instead of an "A" or "F". Hope that helps!
(1 vote)
• The bi-modal graph example (to do with high temperatures), how many groups of data is in that graph, and how would one understand that graph?
• Each bar tells us the amount of days the daily high temperature was within a certain interval.
For example, the third bar from the left says that there were 8 days with a daily high temperature between 5 and 7.5 °C.

My guess is that the left half of the graph are mostly winter days, while the other half are mostly summer days, in which case the temperature a typical winter day would be somewhere around 5 °C, and in the summer more like 25 °C.
• How would trimodal look like?
• A trimodal graph, as the name suggests, would have three "peaks," or places where a lot more data points are clustered around.
(1 vote)
• What is the exact meaning of an outlier?
• Can someone please explain the concept to me?
• Do you only describe the data as bimodal or unimodal if its symmetric or are there other instances that you would describe the data as bimodal or unimodal? (Basically, when would you use those certain shapes?)