1. Describing Distributions
Math 1
Describing Distributions

2. Warm-up
Answer: x < -9/4

3. Shape: Number of Modes
One way to describe the shape of a distribution is by its number of peaks, or modes.
Uniform distribution—has no mode because all data values have the same frequency.

4. Shape: Any peak is considered a mode, even if all peaks do not have the same height.
A distribution with a single peak is called a single-peaked, or unimodal, distribution.
A distribution with two peaks, even though not the same size, is a bimodal distribution.
What is the following distribution?

5. Shape: Symmetry or Skewness
A distribution is symmetric if its left half is a mirror image of its right half.
A symmetric distribution with a single peak and a bell shape is known as a normal distribution.

6. Shape: Symmetry or Skewness
A distribution is left-skewed
(or negatively skewed) if the values
are more spread out on the left,
meaning that some low values are
likely to be outliers.
A distribution is right skewed
or positively skewed if the
values are more spread out
on the right. It has a tail
pulled toward the right.

10. Outliers:
Always report outliers, or data values that are distant from the rest of the observations.

11. Center:
For symmetric distribution, use the mean.
For skewed distribution, use the median.

12. Spread:
When reporting the mean as a measure of center, use the standard deviation for spread.
When reporting the median as a measure of center, use the IQR for spread.

13. To summarize--
When describing a distribution always address SOCS:
S = Shape
O = Outliers
C = Center
S = Spread

14. Class: Wait Times (minutes)
a) Fill in the following table:
Class: Wait Times (minutes)
Tally
Frequency
0 – 9
10 – 19
20 – 29
30 – 39
40 – 49
50 – 59
60 – 69
70 – 79
80 – 89
90 – 99

15. b) Construct a histogram of the data using the given wait times range as bins.

16. c) Describe the distribution (SOCS).

17. Independent Practice:
Work on the last problem independently.

18. How many students are in the math class?
List the data in this set.
Describe the distribution (SOCS).