Cheatography
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This particular cheat sheet is made for my specific Statistics and Probability course. Of course, this is for a mathematics course, so if you are in this class or equivalent, there will be some crossovers.
School: Immaculate Heart High School (Los Angeles)
1.1 Statistics: The Science and Art of Data
Individuals |
The person or thing described in the data set |
Variables |
Any attribute for the individuals that can vary
there are two types of variables |
Categorical Variable |
Has a label (favorite color) |
Quantitative Variable |
Numerical Value and makes sense to find an average (age) |
Frequency table |
Shows the count of each data point (Blue: 10) |
Relative Frequency table |
Shows the percentage of each data point. |
Percentage Formula |
(Part/Whole)x100 |
Dot Plots |
Each dot reprecents one data point (don't skip values that don't have data points |
1.3-4: Displaying Quantitative Data
Skewed Left |
The tail is on the left (more data is on the right) |
Skewed Right |
The tail is on the right (more data is on the left) |
Symmetrical |
The data is split evenly (if you folded it, it would be similar) |
Shape |
Skewed left/right or symmetric |
Center |
The typical value in the data set |
Variability |
How spread out the data is (Variability from __ to __) |
Outliers |
Values significantly far from the others |
In context |
Always connect the description to the actual scenario or context of the data |
Described in context |
The dot plot represents the number of books read last summer. The data is skewed to the right. The center is around around 1-2 books read last summer. The number of books read varies from 0 to 9 books. There is an outlier of 9 books. |
Stemplots |
Stem and leaf plots organize quantitative data using the digits of the values |
Leaf |
The last number/digit of the data point |
Stem |
the other numbers before the last number/digit |
Split Stemplot |
when each stem has too many data point the stems can be split in two: leaves 0-4 and leaves 5-9 |
Info for stemplots |
- Don't skip stems even if they don't have any leaves!
- Always include a KEY!! |
Back-to-Back Stemplot |
To compare two groups of data you can create a stemplot with leaves on either side. The left represents one group of data and the other side represents the other group |
1.7: Measuring Variability
Standard Deviation (Sx) |
The average distance from the mean |
Formula: Sx |
For the sake of your sanity PLEASE use your calculator |
Interquartile Range (IQR) |
The range of the middle 50% of the data |
Formula for IQR |
IQR=Q3-Q1 |
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1.2: Displaying Categorical Data
Bar Charts |
each bar represents one category and the frequency or relative frequency (Helps compare data side by side) |
Pie Chart |
the circle represents the whole data set and each wedge represents the relative frequency of a category. Represents data as a part of a whole |
Deceptive graphs |
Some representation of data are created to manipulate the perception of the data (Always check the scales on a chart and beware of pictographs) |
1.5: Displaying Quantitative Data
Step 1 |
Divide your data into equal intervals |
Step 2 |
Create a frequency table for each interval |
Step 3 |
Label the axis. Label the horizontal axis with the intervals |
Step 4 |
Draw the bars for each interval. (no gaps) |
Notes on Histograms |
The interval contains the first value but not the last |
Relative Frequency histogram |
- Use the same steps but with a relative frequency table
- When made correctly, all the bars in a histogram should add up to 100% or 1 |
Shape |
Skewed left/right or symmetric |
Center |
The typical interval in the data set |
Variability |
How spread out the data is |
Outliers |
intervals significantly far from the others |
1.6: Measuring Canter
Mean |
The average value of a data set |
Median |
The value in the middle of a data set |
Symmetric |
Mean ≈ Median
- use the mean for center |
Skewed Right |
Mean > Median
- use the median for center |
Skewed Left |
Mean < Median
- use the median for center |
Notes on Mean vs. Median |
If there are outliers, use median for center since median is resistant to outliers. Mean is not resistant to outliers |
Mode |
The number that appears the most |
Range |
The difference between the highest and lowest data values |
Quartiles |
Dividing a data set into four intervals |
First (Lower) Quartile |
The middle of the lowerr half of the data set. The first quarter |
Second Quartile (Median) |
Middle Value. The second Quarter of half |
Third (Upper) Quartile |
Middle of the upper half of the data set. The third quarter |
1.8: Boxplots and Outliers
Boxplots |
displays data using Min, Max, Q1, Q3, median, and outlier values |
Step 1 |
Create a numberline from the variability of the data |
Step 2 |
Make the Q1, Median, and Q3. draw a box between Q1 and Q3 with a line through the median |
Step 3 |
Mark the Min and Max (excluding the outlier values) and connect them to the box with a line |
Step 4 |
Add * to mark the high and low outliers |
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