Question Types and Data Displays
This type of question anticipates different answers from different people and can be answered by collecting data.
What is a statistical question?
This type of distribution has all values or outcomes occurring with roughly equal frequency and often appears as a flat, level shape.
What is a uniform distribution?
This measure of center is found by adding all the values and dividing by the number of values.
What is mean?
This is a data value that is unusually far from the other values in a distribution.
What is an outlier?
When comparing two data sets, what can be said about a distribution with values that are more spread out?
What is higher variability?
“What type of transportation do students use to get to school?” collects this type of data.
What is categorical data?
When most values are clustered at the lower end and the tail extends toward higher values, the distribution has this shape.
What is a right-skewed distribution?
Find the interquartile range of this ordered data set: 4, 6, 7, 9, 10, 12, 15, 18.
What is an IQR of 7?
Identify the possible outlier in this data set: 3, 4, 5, 5, 6, 20.
What is 20?
When comparing two symmetric data sets, how can you determine which data set has greater variability without looking at a display?
What is a greater standard deviation or MAD?
“How many minutes does it take students to get to school?” collects this type of data.
What is quantitative data?
A distribution has a long tail extending toward smaller values. It is described as having this shape.
What is a distribution skewed left?
A data distribution is fairly symmetric with no apparent outliers. Which measure of center and which measure of variability are appropriate for describing this distribution?
What are the mean and mean absolute deviation/standard deviation?
A data set has one unusually large value. Which measure of center will usually be affected more by that value: the mean or the median?
What is the mean?
Class A has a median test score of 78 and an IQR of 12. Class B has a median of 84 and an IQR of 5. Which class has the higher typical score, and which class has more variability?
What is Class B for the higher typical score and Class A for the greater variability?
This display is especially useful for showing the individual values and overall shape of a small quantitative data set.
What is a dot plot?
In this type of distribution, the left and right sides have approximately the same shape and spread around the center.
What is a symmetric distribution?
A data distribution is clearly skewed right and contains an unusually large value. Which measure of center and which measure of variability are appropriate for describing this distribution?
What are the median and interquartile range?
When should an outlier be excluded from a data set?
What is when it was an error?
Two data sets have the same median. Data Set A has an IQR of 4, and Data Set B has an IQR of 15. Which data set is more consistent, and why?
What is Data Set A, because its smaller IQR shows less variability in the middle half of the data
The display that divides the data into four equal sections is this.
What is a box plot?
A histogram of test scores has two distinct clusters: one near 60 and another near 90.
What is a bimodal distribution?
Find the mean absolute deviation of the data set: 2, 4, 4, 6.
What is a mean absolute deviation of 1?
Using the 1.5*IQR rule, show work for identifying the outlier in this data set: 1, 2, 3, 4, 5, 6, 7, 20.
The lower quartile is 2.5, the upper quartile is 6.5, and the IQR is 4. The upper bound is 6.5+1.5(4)=12.5, so 20 is an outlier.
The following statistics were calculated for two skewed data sets:
Data Set A:
mean: 10 median: 16 standard deviation: 6 IQR: 9
Data Set B:
mean: 12 median: 14 standard deviation: 5 IQR: 11
Which data set has a higher measure of center and which has a higher measure of variability?
What is Data Set A has a higher measure of center (using median) and Data Set B has a higher measure of variability (using IQR).