Arrange the `POINTS` orange points on the number line so the
arithmetic mean is

and the median is `MEAN`

.
The distance between adjacent tick marks is 1.`MEDIAN`

graph.targetMedian = MEDIAN;
graph.targetMean = MEAN;
graph.numPoints = POINTS;
init({
range: [ [LOWER_BOUND - 1, UPPER_BOUND + 1], [-3, 3] ]
});
style({ stroke: "#bbb" });
line( [ LOWER_BOUND, 0 ], [ UPPER_BOUND, 0 ] );
for ( var x = LOWER_BOUND; x <= UPPER_BOUND; x++ ) {
line( [ x, -0.2 ], [ x, 0.2 ] );
}
style({ strokeWidth: 3.5 });
line( [ 0, -0.2 ], [ 0, 0.2 ] );
label( [ 0, -0.53 ], "0", "center", {});
style({ strokeWidth: 2, stroke: BLUE, fill: BLUE, opacity: 1.0 });
graph.meanArrow = path([
[ 0, 0.7 ], [ 0.05, 0.7 ], [ 0, 0.6 ], [ -0.05, 0.7 ], [ 0, 0.7 ], [ 0, 1.0 ]
]);
graph.meanLabel = label( [ 0, 1.3 ], "\\text{mean}", "above", { color: BLUE });
graph.meanValueLabel = label( [ 0, 0.8 ], "0", "above", { color: BLUE });
style({ strokeWidth: 2, stroke: GREEN, fill: GREEN });
graph.medianArrow = path([
[ 0, -1.1 ], [ 0.05, -1.1 ], [ 0, -1 ], [ -0.05, -1.1 ], [ 0, -1.1 ], [ 0, -1.4 ]
]);
graph.medianLabel = label( [ 0, -1.7 ], "\\text{median}", "below", { color: GREEN });
graph.medianValueLabel = label( [0, -1.2 ], "0", "below", { color: GREEN });
addMouseLayer();
graph.points = [];
for ( var x = 0; x < POINTS; x++ ) {
graph.points[x] = addMovablePoint({
coord: [ x - POINTS / 2 + 0.5, 0 ],
constraints: { constrainY: true },
snapX: 0.5
});
}
graph.median = 0;
graph.mean = 0;
jQuery.each( graph.points, function( idx, point ) {
this.onMove = function( x, y ) {
return onMovePoint( point, x, y );
};
});

Move the orange dots to select your answer.

The median is middle number. In other words there are always as many points to the right of the median as to the left.

Try dragging the points so that half of them are to the left of

and half of them are to the right of
`MEDIAN`

.
The two points in the middle should be the same distance from
`MEDIAN`

.
The middle point should be at
`MEDIAN`

.
`MEDIAN`

As long as there are as many points to the left and to the right of the median, the median will stay the same. But the arithmetic mean is calculated using the value of every point. Try moving the points on either side of the median closer and further from the median to see how the mean is affected.

There are a number of different ways to arrange the points so the mean is

and the median is
`MEAN`

.
`MEDIAN`