Statistical Questions

Common Core Standard: Recognize a statistical question as one that anticipates variability in the data related to the
question and accounts for it in the answers.

Common Core Standard: Understand that a set of data collected to answer a statistical question has a distribution
which can be described by its center, spread, and overall shape

Statistical question – is a question that requires data for the answer

Example: Determine which the following is a statistical question and why
o
How old am I?
o
How old are the students in my school?

The first question is not a statistical question, because there is only one answer, which does not
require data

The second question is a statistical question, because you would need to compile data regarding
the ages of all the students in the school

Variability – how data changes

Distribution – how the data is spread out along the graph

Note: All types of graphs can be analyzed using these methods

Measures of Center – are numbers that best describe the center of the data: mean, median, or mode

o
Mean - is the average (add all the numbers then divide by how many numbers there are)
o
Median – is the middle number, when the data is arranged in order from least to greatest
o
Mode – is the most commonly occurring number
Knowing the spread and overall shape of the graph will enable us to determine how far apart the data is and if the
data is clustered in any particular spot on the graph

Cluster – is a group of data

Example: Determine the overall shape of the data below and identify if any clustering is apparent. Also, determine
all measures of center.
o
The graph is clustered between 6 and 7
o
The shape of the graph is mostly spread out except for the cluster between 6 and 7, most of the data is
located there
o
There is no outlier present in the data
o
Mean:
o
o

5 + 5.5 + 6 + 6 + 6 + 6.5 + 6.5 +6.5 +6.5 +7 + 7 + 8 + 8 + 9 = 93.5

93.5 ÷ 14 = approximately 6.68
Median:

5, 5.5, 6, 6, 6, 6.5, 6.5, 6.5, 6.5, 7, 7, 8, 8, 9

6.5 and 6.5 are the middle numbers, so the median is the average of these numbers

6.5 + 6.5 = 13; 13 ÷ 2 = 6.5

Thus, the median is 6.5
Mode:

o
The number that occurs the most often is 6.5
Since, all three measures of center are close, you can use any of these values as the measure of center