Presenting Quantitative Data Graphically
Quantitative, or numerical, data can also be summarized into frequency tables.Example 9
A teacher records scores on a 20-point quiz for the 30 students in his class. The scores are: 19 20 18 18 17 18 19 17 20 18 20 16 20 15 17 12 18 19 18 19 17 20 18 16 15 18 20 5 0 0 These scores could be summarized into a frequency table by grouping like values:Score | Frequency |
0 | 2 |
5 | 1 |
12 | 1 |
15 | 2 |
16 | 2 |
17 | 4 |
18 | 8 |
19 | 4 |
20 | 6 |

Histogram
A histogram is like a bar graph, but where the horizontal axis is a number lineExample 10
For the values above, a histogram would look like:
Class Intervals
Class intervals are groupings of the data. In general, we define class intervals so that:- Each interval is equal in size. For example, if the first class contains values from 120-129, the second class should include values from 130-139.
- We have somewhere between 5 and 20 classes, typically, depending upon the number of data we’re working with.
Example 11
Suppose that we have collected weights from 100 male subjects as part of a nutrition study. For our weight data, we have values ranging from a low of 121 pounds to a high of 263 pounds, giving a total span of 263-121 = 142. We could create 7 intervals with a width of around 20, 14 intervals with a width of around 10, or somewhere in between. Often time we have to experiment with a few possibilities to find something that represents the data well. Let us try using an interval width of 15. We could start at 121, or at 120 since it is a nice round number.Interval | Frequency |
120 - 134 | 4 |
135 – 149 | 14 |
150 – 164 | 16 |
165 – 179 | 28 |
180 – 194 | 12 |
195 – 209 | 8 |
210 – 224 | 7 |
225 – 239 | 6 |
240 – 254 | 2 |
255 - 269 | 3 |



Try it Now 3
The total cost of textbooks for the term was collected from 36 students. Create a histogram for this data. $140 $160 $160 $165 $180 $220 $235 $240 $250 $260 $280 $285 $285 $285 $290 $300 $300 $305 $310 $310 $315 $315 $320 $320 $330 $340 $345 $350 $355 $360 $360 $380 $395 $420 $460 $460 When collecting data to compare two groups, it is desirable to create a graph that compares quantities.Example 12
The data below came from a task in which the goal is to move a computer mouse to a target on the screen as fast as possible. On 20 of the trials, the target was a small rectangle; on the other 20, the target was a large rectangle. Time to reach the target was recorded on each trial.Interval (milliseconds) | Frequency small target | Frequency large target |
300-399 | 0 | 0 |
400-499 | 1 | 5 |
500-599 | 3 | 10 |
600-699 | 6 | 5 |
700-799 | 5 | 0 |
800-899 | 4 | 0 |
900-999 | 0 | 0 |
1000-1099 | 1 | 0 |
1100-1199 | 0 | 0 |

Frequency polygon
An alternative representation is a frequency polygon. A frequency polygon starts out like a histogram, but instead of drawing a bar, a point is placed in the midpoint of each interval at height equal to the frequency. Typically the points are connected with straight lines to emphasize the distribution of the data.Example 13
This graph makes it easier to see that reaction times were generally shorter for the larger target, and that the reaction times for the smaller target were more spread out.