Data Visualizations
When is it appropriate to use a bar chart vs histogram to represent data?
Bar chart = categorical variable; Histogram for numerical variable
Unimodal vs Bimodal vs Multimodal
1 peak vs 2 peaks vs 3 or more peaks
Explain how to find each measure of center (mean, median, mode)
Mean= Total of data values divided by the number of data in set; Median = sort data from least to greatest, "middle number"; Mode = most frequent occurrence in data set
n
number of values
Which measures of center and spread are preferentially used to describe normally distributed data?
Mean and Standard Deviation
In a histogram or bar chart, the vertical axis represents frequency. What's the difference in relative frequency and (quantitative) frequency.
(quantitative) frequency = raw counts of data; relative frequency = percentages so all bars added together should equal 100%
Left =tail to the left, Right = tail to the right, symmetrical = bell-shaped
Explain how to find the IQR given a list of values.
Put in order, find Q1 and Q3, then subtract Q3-Q1.
(pronounced mu)
population mean
Which measures of center and spread are preferentially used to describe skewed data?
Median and IQR
In creating bins for a histogram, bin sizes must be ...
evenly spaced (same amount in each range)
Distribution where mean=median=mode (or very close)
Roughly symmetrical
Using your notes, explain the processes of calculating the standard deviation.
Find the mean, subtract the mean from each value, square each, add, divide by n-1, square root.
(pronounced x bar)
sample mean
What does it mean for a sample to have a standard deviation of zero?
There is no variability in the data (only a single score)
When deciding how many bins to use in a histogram, what is the general idea you must keep in mind?
You want enough bins to be able to identify the shape of the distribution.
2 Distributions:
one where the mean > median; other where mean < median
One mean > median = right-skewed; other mean < median = left-skewed
How do you calculate the mean of a frequency chart?
You multiply each value times its frequency, add up those totals, then divide by how many data points you have.
Greek letter Sigma
the summation of
A student was making calculations of center and spread on a set of data from a survey question response: {2, 2, 4, 1, 3, 2, 1, 2, 7}. After calculating, one last survey response came in late with a response answer of 12. Needing to recalculate the center and spread, what calculations will/will not change: IQR? S.D.? Mean? Median?
Median will be the only one that will not change.
In labeling the histogram horizontal axis, the number on the marks at the end point of the bin indicate...
the maximum value included in the bin.
Create a boxplot with the given data (include 5 number summary)
7, 5, 11, 10, 2, 13, 9
Min = 2, Q1 = 6, Med = 9, Q3 = 10.5, Max = 13
How do you calculate the median, Q1, and Q3 of a frequency chart?
You count from one end to the other, identifying which bin contains the halfway point, the 25th percentile, and the 75th percentile, respectively.
s2
Variance (when finding standard deviation it's what you are taking the square root of)
In a open-ended question, if it asks you to describe a distribution, what all must you have detailed accurately in your written conclusion for full credit?
Center (mean or median), Unique features (outliers, modality), Shape (skewed etc.), Spread (S.D. or IQR) used within context. (Only time Mrs. Zachary encourages anyone to CUSS.)