Mean Mania
What does the mean represent in a data set?
The equal share value.
Which graph is best for categorical data ?
Bar graph.
Center, variability, and shape
Name one measure of variability.
Range, IQR, or MAD
Define median.
The middle value when the data is ordered.
Find the mean 2,4,6,8
5
Which graphs are used for numerical data?
Dot plots, histograms, and box plots.
If data is symmetrical, which measure of center should you use?
Mean
What does the range show?
The difference between the highest and lowest values.
Define mode.
A class's test scores are 70,80,85,90,100. If the teacher adds a new score of 0, what happens to the mean?
The mean decreases a lot.
In a histogram, if most data is on the left and a few bars stretch far to the right, how is the data shaped?
Skewed Right
If data is skewed, which measure of center is best?
Median
Why do we calculate IQR ?
To measure the spread of the middle 50% of data.
A box plot shows a very long whisker on the right side. What does this mean?
The data is skewed right.
Which measure changes more when extreme values are added: mean or median ?
Mean
A box plot shows Q1=20 and Q3=40 , what is the IQR ?
20
A class survey shows a mean of 2 siblings per student, but most students have 1 or 2 siblings, and one student has 10. Which measure ( mean or median) better represents the data? Why?
Median, because the mean is pulled up by the outlier.
Which measure of variability shows the spread around the mean?
Mean Absolute Deviation (MAD).
Why does a symmetrical distribution allow you to use mean and median interchangeably?
Because they are approximately the same when the data is balanced.
A teacher wants to show typical performance on a skewed test set with one very low score. Should she use mean or median, and why?
Median, because it is less affected by outliers.
A dot plot of student absences is very spread out. What does this tell us about the consistency of student attendance?
It is inconsistent, and attendance varies widely.
Create a possible data set that would have a mean of 10 but a median of 5.
example : 1,2,5,20,22
Two classes took the same test. Both had a mean of 80. Class A had an IQR of 10, while Class B had an IQR of 25. What does this mean about their test performance?
Class A had more consistent test scores. Class B had more varied scores.
Compare two histograms. Class A is symmetrical, Class B is skewed right. If both have the same mean, which class likely has more consistent data?
Class A because a symmetrical graph is more balanced and consistent.