Mean, median and mode explorer

What the explorer shows

Each dot is one value on a number line from 0 to 20. Dots with the same value stack up, like a dot plot. Drag a dot to change its value, or select it and use the arrow keys or the move buttons. You can add dots up to 15, remove the selected dot, or add an outlier at 20.

The mean sits under the line as a triangle, because the mean is the balance point: if the dots were weights on a seesaw, the line would balance there. The median is the purple marker above, and the middle value or values are highlighted in the row of sorted numbers underneath. Mode dots turn yellow. You can hide any of the three to predict first.

Why drag the data

Students often learn three recipes and mix them up. Moving the data and watching the averages respond shows what each one measures. The median only cares about order, so moving the biggest value further right does nothing to it. The mean uses every value, so one extreme value pulls it along. The balance-point challenge makes this physical: the beam tilts toward the heavier side until the triangle sits at the mean.

Common mix-ups

• Finding the median without putting the values in order first. The sorted row shows why order matters.
• Thinking the mean must be one of the values. A mean of 6.43 is fine even when every value is a whole number.
• Expecting every data set to have one mode. Some have two, and if every value appears equally often there is no mode.
• Thinking an outlier moves all averages the same amount. It usually pulls the mean much more than the median.

A 10-minute averages lesson

• Turn off all three markers. Ask students to find the mean, median and mode of the starting dots on paper.
• Turn them back on to check.
• Press Add an outlier at 20. Ask which average changed more, and why.
• Ask: if these were test scores, which average describes a typical score better now?
• Finish with a challenge from New challenge.

Where it fits by grade

• Grade 6: a measure of center summarizes data with one number (6.SP.A.3), data is shown in dot plots (6.SP.B.4), and students describe center and spread and any values that stand out (6.SP.B.5c), choosing measures that suit the data (6.SP.B.5d).
• Grade 7: compare two data sets using measures of center and variability (7.SP.B.4).
• England: Year 6 calculates and interprets the mean as an average, and Key Stage 3 adds the median, mode and range and considers outliers.

Learning more

Division and decimals, which the mean depends on, are skills on Eurekami's skill map, and Daily Practice brings them back when they start to fade. Exam Prep includes GCSE Maths practice papers, and the AI tutor asks guiding questions when a statistics problem is tricky.