Describing Data
The value of a quantitative variable that appears most often in the data.
The mode!
A bar graph should only be used for this kind of data.
Categorical
The mean of this data:
2, 5, 10, 12, 17, 20
11
The value with p% of the observations less than it.
Pth percentile
This kind of variable measures the outcome of a study or experiment.
Response Variable
A distribution with two clear peaks is called this.
Bimodal
In this graph, each observation is shown as a dot above its value.
Dotplot
A statistic that is not influenced by extreme observations.
Resistant Measure
150 is an observation from a N(50,25) distribution.
This is the z-score.
4
We discuss these four characteristics when describing the pattern of a scatter plot.
DOFS!
Direction, outliers, form, and strength.
In a distribution with this shape, the mean is always less than the median.
Left-skewed
This is why you might want to split the stems on a stemplot.
The IQR of this data:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
5
A distribution is bimodal and left-skewed. Its mean is 35 and its standard deviation is 9. We subtract 35 from each observation and divide by 9.
This is the new distribution's shape.
This kind of variable cannot be analyzed using correlation.
Categorical
These are the four components should we discuss when describing the overall pattern of a distribution.
SOCS!
Shape, outliers, center, and spread.
When quantitative variables take on many different values, we should use this kind of graph.
Histogram
Find the standard deviation of this data:
7, 7, 9, 9
1
The distribution of adult men measured in inches is approximately N(69,2.5).
This is the percent of men taller than 74 inches.
2.5%
This kind of variable is always plotted on the horizontal axis.
Explanatory
A distribution with many more observations to the right side of the mode than the left.
Right-skewed
If you want to compare two distributions with a stemplot, you might make this kind of graph.
Back-to-back stemplot
You can only use integers from 0 to 10. Repeats are allowed.
Choose 4 numbers that have the largest possible standard deviation.
0, 0, 10, 10
The distribution of adult men measured in inches is approximately N(69,2.5).
This is the percent of men between 64 and 66.5 inches tall.
13.5%
A correlation of exactly -1 means this.
All observations are on a negatively-sloped line.