Measures of Center
What is the mean of the data set: 4,6,7,8,10
7
How do you find the range of a data set?
Subtract the minimum from the maximum.
What type of graph is best for showing the data over intervals?
Histograms
A survey shows 60% of students prefer chocolate milk. How can this be misleading?
If the sample size is small, it may not represent all of the students.
A distribution has a mean of 25 and a median of 18. What does this suggest?
The data is skewed right
Find the median of 8,3,12,5,18,15
10
Find the range of 10,21,7,3,14, 12,4
18
What does a box plot display?
The median, the quartiles and outliers
What is one reason for using a histogram instead of a bar graph?
Histograms show the distribution over intervals.
The outlier lowered the mean significantly
What happens to the mean if you add an extreme outlier to the data set?
The mean increases or decreases significantly, depending on the outlier.
What does the interquartile range (IQR) measure?
The spread of the middle 50% of data (Q3-Q1)
A dot plot had three peaks. What does this tell us?
The data is multimodal (had multiple modes)
A company claims the "average" salary is $90,000 but most employees earn $50,000. What's misleading>
The mean is skewed by the higher salaries which may be outliers (better to use the median)
Why might a box plot be better than a histogram?
A boxplot clearly shows spread, quartiles and outliers.
A student scores 92, 65, 85, 78,95 on test. What is the mode?
There is no mode
What is the mean absolute deviation (MAD) used for?
It measures how far each data point is from the mean.
If a histogram is skewed right, what does this mean about the data?
Most values are lower with a few high outliers
If a graph shows test scores with a large standard deviation, what does that mean?
Scores vary widely from the mean
A dataset has a high IQR but a low range. What does this suggest?
The middle 50% is widely spread, but the extreme values are close
An American football player's yardage per game is 40,50,50,55,60,70. If the 70-yard game is removed, how does this affect the mean?
The mean will decrease.
A data set has an IQR of 12 and a range of 24. What does this tell us?
The middle 50% of the data is more tightly grouped compared to the total range.
If a box plot has a very short right whisker and a long left whisker, what does it suggest?
The data is skewed left
How can you tell if real world data is biased?
If it was collected unfairly or from a non-representative group.
A factory produces widgets with an average weight of 10grams and a MAD of 0.5 grams. Why is this important?
The MAD shows consistent production quality