Histogram

Lina and Maria, have measured the height of their friends. They have listed the results in a table. Now they want to find out what height is most common. To make it easier to see, they decide to make a picture, a graph, of the table. The horizontal axis shows the different friends.

The vertical axis shows height, in centimetres. Then they make a rectangle, a bar, showing the height of each friend. They have asked 19 friends, so there are 19 bars. But everyone is different heights! There aren’t two friends that are exactly the same height, so no height is most common!

All heights occur only once. Lina is thinking… ...that it may be better to sort the lengths in groups: Those between 130 and 140 centimetres form one group. Those who are between 140 and 150 centimetres form the next group, and so on. We call these groups intervals. Lina and Maria then mark how many friends are in each interval.

What if someone is exactly 140 centimeters? Then, that friend ends up in the interval 140 to 150 centimeters—upwards. Three friends are between 130 and 140 centimetres tall. Between 140 and 150 centimetres? Six friends.

150 to 160: one, 160 to 170: two, 170 to 180: five, and between 180 and 190 centimetres, two friends. They draw a new graph. Now, the height in centimetres is displayed on the horizontal axis. Since none of the friends are shorter than 130 centimetres, they contract the axis between zero and 130 centimetres. They show this with a small zigzag notch on the axis.

Then they enter the boundaries for all the intervals. 130, 140, 150, up to 190. The vertical axis shows the number of friends in each interval. Look at the table. Lina and Maria have three friends who are between 130 and 140 centimetres tall.

Then they are included in the bar for the interval 130 to 140 centimetres. The height of that bar is three friends. The next row in the table shows that there are six friends in the interval 140 to 150 centimetres. When the horizontal axis is divided into intervals, like this, and the bars show how many are in each interval, then the graph is called a histogram. Now we finish drawing the histogram.

In the next interval, 150 to 160 centimetres, there is just one person, so the bar goes to one. After that, two friends, then five friends. And the last bar. It is two persons high. The histogram now looks like this: All bars are equally wide, since each interval is the same size, 10 centimetres, on the horizontal axis.

Now Lina and Maria can easily get an overall picture of how tall their friends are. And most of their friends are between 140 and 150 centimetres tall.