Distribution shape describes the overall pattern of how data values are spread when displayed in a histogram or dot plot. Common shapes include symmetric (bell curve), skewed left, skewed right, uniform (all values equally common), and bimodal (two peaks).
If you make a histogram, what shape emerges? A bell curve? A slope leaning one way? Two peaks? The shape tells you about what's typical and what's unusual in your data.
Showing a random 20 of 50 problems.
Example 1
easy
In a SYMMETRIC distribution, the mean is __ the median.
Example 2
hard
A data set has mean 20, median 20, and one cluster between 5 and 35 with no extreme tail. Is the most likely shape uniform or symmetric unimodal?
Example 3
challenge
A distribution is perfectly symmetric and bimodal (two equal peaks). Where do its mean and median fall relative to the two peaks?A perfectly symmetric bimodal distribution — where do mean and median fall relative to the two peaks?
Example 4
hard
True or false: every bimodal distribution must have equal-height peaks.
Example 5
medium
Classify each distribution shape: (a) Test scores cluster around 75 with equal tails. (b) Marathon finish times have a peak at 4 hours with a long tail for slower runners. (c) Ages at a family reunion show peaks at 10 and 40.
Example 6
medium
A uniform distribution over equally likely values has what skewness and mean-median relationship?
Example 7
medium
A histogram of ages at a children's birthday party shows two peaks: one around age 7 (kids) and one around age 35 (parents). What shape?
Example 8
easy
A fair die is rolled 6000 times and outcomes counted. What shape does the histogram of outcomes have?
Example 9
medium
A test with mean 75 and median 82 is what shape?
Example 10
easy
A histogram is a mirror image about its center peak. What shape is it?A histogram that is a mirror image about its center peak — what shape is this?
Example 11
medium
A bimodal histogram of student heights mixes two grade levels. What does the shape suggest about the data?Heights from two mixed grade levels — two peaks. What does this bimodal shape suggest?
Example 12
easy
A distribution has a long tail stretching to the LEFT. What is its skew?This distribution has a long tail stretching to the LEFT — what is its skew?
Example 13
medium
Roll two fair dice and sum. Which shape best describes the histogram of sums from 2 to 12?
Example 14
medium
Shoe sizes for a school of 400 students. What is the most likely shape?
Example 15
easy
A distribution has a long tail stretching to the RIGHT (toward large values). What is its skew?This distribution has a long tail stretching to the RIGHT — what is its skew?
Example 16
medium
For a right-skewed distribution, which is generally larger: the mean or the median?
Example 17
medium
Test scores where almost everyone scored very high and a few scored low. What skew?Almost everyone scored high; a few scored low — what skew does this create?
Example 18
hard
Data: 10,12,15,15,17,18,20. Compare mean and median to identify the shape.
Example 19
easy
A dot plot shows clusters around 5 and 25 with very few values in between. What shape is this?
Example 20
challenge
Distribution A is symmetric; distribution B is right-skewed. Both have median 50. Which has the larger mean, and why?