An extension of histogram interpretation: estimating within a class using an even-spread assumption. Exact requirements vary by course.
- Recover class frequencies from bar areas and form a cumulative total.
- Locate N/2. In the median class, find what fraction of that class’s frequency you still need.
- Estimated median = lower boundary + fraction through class × class width. This assumes an even spread.
Example 1
Estimate the median to 1 d.., assuming values are evenly spread within each class.
f = frequency; CF = cumulative frequencyBlack: given data. Blue: working we add.
Median positionFor a grouped-data estimate, locate halfway through the total frequency. Fraction through classSubtract the frequency before the median class, then divide by its frequency. Estimated medianStart at the lower class boundary and move this fraction of the class width. Estimated medianAssume an even spread within the class. Round the final estimate to 1 d.. Example 2
Estimate the median to 1 d.., assuming values are evenly spread within each class.
f = frequency; CF = cumulative frequencyBlack: given data. Blue: working we add.
Median positionFor a grouped-data estimate, locate halfway through the total frequency. Fraction through classSubtract the frequency before the median class, then divide by its frequency. Estimated medianStart at the lower class boundary and move this fraction of the class width. Estimated medianAssume an even spread within the class. Round the final estimate to 1 d.. Your turn
Question 1Estimate the median to 1 d.., assuming values are evenly spread within each class.
Check answer
f = frequency; CF = cumulative frequencyBlack: given data. Blue: working we add.
Median positionFor a grouped-data estimate, locate halfway through the total frequency. Fraction through classSubtract the frequency before the median class, then divide by its frequency. Estimated medianStart at the lower class boundary and move this fraction of the class width. Estimated medianAssume an even spread within the class. Round the final estimate to 1 d.. Question 2Estimate the median to 1 d.., assuming values are evenly spread within each class.
Check answer
f = frequency; CF = cumulative frequencyBlack: given data. Blue: working we add.
Median positionFor a grouped-data estimate, locate halfway through the total frequency. Fraction through classSubtract the frequency before the median class, then divide by its frequency. Estimated medianStart at the lower class boundary and move this fraction of the class width. Estimated medianAssume an even spread within the class. Round the final estimate to 1 d.. Question 3Estimate the median to 1 d.., assuming values are evenly spread within each class.
Check answer
f = frequency; CF = cumulative frequencyBlack: given data. Blue: working we add.
Median positionFor a grouped-data estimate, locate halfway through the total frequency. Fraction through classSubtract the frequency before the median class, then divide by its frequency. Estimated medianStart at the lower class boundary and move this fraction of the class width. Estimated medianAssume an even spread within the class. Round the final estimate to 1 d.. Question 4Estimate the median to 1 d.., assuming values are evenly spread within each class.
Check answer
f = frequency; CF = cumulative frequencyBlack: given data. Blue: working we add.
Median positionFor a grouped-data estimate, locate halfway through the total frequency. Fraction through classSubtract the frequency before the median class, then divide by its frequency. Estimated medianStart at the lower class boundary and move this fraction of the class width. Estimated medianAssume an even spread within the class. Round the final estimate to 1 d.. Question 5Estimate the median to 1 d.., assuming values are evenly spread within each class.
Check answer
f = frequency; CF = cumulative frequencyBlack: given data. Blue: working we add.
Median positionFor a grouped-data estimate, locate halfway through the total frequency. Fraction through classSubtract the frequency before the median class, then divide by its frequency. Estimated medianStart at the lower class boundary and move this fraction of the class width. Estimated medianAssume an even spread within the class. Round the final estimate to 1 d.. Estimate the median to 1 d.., assuming values are evenly spread within each class.
Answerf = frequency; CF = cumulative frequencyBlack: given data. Blue: working we add.
Median positionFor a grouped-data estimate, locate halfway through the total frequency. Fraction through classSubtract the frequency before the median class, then divide by its frequency. Estimated medianStart at the lower class boundary and move this fraction of the class width. Estimated medianAssume an even spread within the class. Round the final estimate to 1 d.. Estimate the median to 1 d.., assuming values are evenly spread within each class.
Answerf = frequency; CF = cumulative frequencyBlack: given data. Blue: working we add.
Median positionFor a grouped-data estimate, locate halfway through the total frequency. Fraction through classSubtract the frequency before the median class, then divide by its frequency. Estimated medianStart at the lower class boundary and move this fraction of the class width. Estimated medianAssume an even spread within the class. Round the final estimate to 1 d.. Estimate the median to 1 d.., assuming values are evenly spread within each class.
Answerf = frequency; CF = cumulative frequencyBlack: given data. Blue: working we add.
Median positionFor a grouped-data estimate, locate halfway through the total frequency. Fraction through classSubtract the frequency before the median class, then divide by its frequency. Estimated medianStart at the lower class boundary and move this fraction of the class width. Estimated medianAssume an even spread within the class. Round the final estimate to 1 d.. Estimate the median to 1 d.., assuming values are evenly spread within each class.
Answerf = frequency; CF = cumulative frequencyBlack: given data. Blue: working we add.
Median positionFor a grouped-data estimate, locate halfway through the total frequency. Fraction through classSubtract the frequency before the median class, then divide by its frequency. Estimated medianStart at the lower class boundary and move this fraction of the class width. Estimated medianAssume an even spread within the class. Round the final estimate to 1 d.. Estimate the median to 1 d.., assuming values are evenly spread within each class.
Answerf = frequency; CF = cumulative frequencyBlack: given data. Blue: working we add.
Median positionFor a grouped-data estimate, locate halfway through the total frequency. Fraction through classSubtract the frequency before the median class, then divide by its frequency. Estimated medianStart at the lower class boundary and move this fraction of the class width. Estimated medianAssume an even spread within the class. Round the final estimate to 1 d..