Mean and Median
What is the mean of the data set: 3, 7, 8, 5, 10?
The mean is 6..6
What does the interquartile range (IQR) measure?
The IQR measures the spread of the middle 50% of the data.
What does standard deviation indicate about a data set?
It indicates how much the data values deviate from the mean.
What is a histogram?
A histogram is a graphical representation of the frequency distribution of numerical data.
What are measures of center?
Measures of center include mean, median, and mode, which summarize the central point of a data set.
How do you find the median in a data set with an even number of values?
The median is the average of the two middle numbers.
How do you calculate the IQR if the quartiles are Q1 = 5 and Q3 = 15?
The IQR is Q3−Q1=15−5=10
If the standard deviation of a data set is 0, what does that tell you?
It tells you that all the data values are the same.
Describe what a box plot displays.
A box plot shows the minimum, first quartile, median, third quartile, and maximum of a data set.
How can you compare two data sets using their means?
By comparing the means, you can determine which data set has a higher average value.
If the mean of a data set is 20 and there are 5 numbers, what is the total sum of the numbers?
The total sum is 20×5=100
What is the significance of the IQR in identifying outliers?
The IQR helps determine outliers by identifying values that fall below Q1−1.5×IQR or above Q3+1.5×IQR
How does a larger standard deviation affect the interpretation of data?
A larger standard deviation indicates more variability and a wider spread of data points around the mean.
Why would you use a dot plot instead of a histogram?
A dot plot is useful for smaller data sets and shows individual data points, making it easy to see frequency.
Why is it important to look at measures of variability when comparing data sets?
Measures of variability show how much the data points differ from the mean, which helps understand the consistency of the data sets.
Define what it means when a data set is skewed to the right.
It means that the majority of the data values are concentrated on the left side with a long tail on the right.
If a data set has an IQR of 8, what does that imply about the data spread?
It implies that the middle 50% of the data values are spread over a range of 8 units.
Calculate the standard deviation for the data set: 4, 8, 6, 5, 3.
The standard deviation is approximately 1.58.
What is the role of the median in a box plot?
The median divides the data into two equal halves and is represented by the line inside the box.
If two data sets have the same mean but different standard deviations, what can you infer?
It means that one data set is more consistent than the other, despite having the same average.
Explain how the mean can be influenced by outliers in a data set.
Outliers can significantly increase or decrease the mean, making it unrepresentative of the majority of data.
Explain the difference between a box plot and a histogram.
A box plot shows the median, quartiles, and potential outliers, while a histogram displays the frequency distribution of data values.
How would you explain the concept of standard deviation to someone unfamiliar with statistics?
Standard deviation is a measure of how spread out the numbers are in a data set; a small standard deviation means the numbers are close to the average, while a large one means they are more spread out.
Explain how to choose the best data display for a given data set.
The best data display depends on the size and type of data; for large data sets, histograms or box plots are useful, while for smaller sets, dot plots might be better.
Describe a scenario where comparing the interquartile range (IQR) of two data sets would be essential.
Comparing the IQR of two data sets can show which one has more variability in the middle 50% of data, which is crucial in fields like education or health assessments where outliers might skew results.