In these lessons, we will learn:

- how to create a frequency table for interval data or grouped data
- how to obtain the mean, median, mode and range from a grouped frequency table
- how to estimate the median and quartiles and percentiles from a grouped frequency table

**Related Pages**

Frequency Tables

Mean And Mode From The Frequency Table

Median From The Frequency Table

More Statistics Lessons

Data may be **discrete** or
**continuous**. Discrete data can only take particular values
(usually whole numbers) such as the number of children per family. Continuous data can take
any value in a given range, for example mass, height, age and temperature.

Sometimes, the collected data can be too numerous to be meaningful. We need to organize data
in some logical manner in order to make sense out of them. We could group data into
**classes**. Each class is known as a
**class interval.**

**Example:**

The data below shows the mass of 40 students in a class. The measurement is to the nearest kg.

55 | 70 | 57 | 73 | 55 | 59 | 64 | 72 |

60 | 48 | 58 | 54 | 69 | 51 | 63 | 78 |

75 | 64 | 65 | 57 | 71 | 78 | 76 | 62 |

49 | 66 | 62 | 76 | 61 | 63 | 63 | 76 |

52 | 76 | 71 | 61 | 53 | 56 | 67 | 71 |

Construct a frequency table for the data using an appropriate scale.

**Solution:**

**Step 1:** Find the range.

The **range** of a set of numbers is the difference between
the least number and the greatest number in the set.

In this example, the greatest mass is 78 and the smallest mass is 48. The range of the masses is then 78 – 48 = 30. The scale of the frequency table must contain the range of masses.

**Step 2:** Find the intervals

The **intervals** separate the scale into equal parts.

We could choose intervals of 5. We then begin the scale with 45 and end with 79

**Step 3:** Draw the frequency table using the selected
scale and intervals.

Mass (kg) | Frequency |
---|---|

45 – 49 | 2 |

50 – 54 | 4 |

55 – 59 | 7 |

60 – 64 | 10 |

65 – 69 | 4 |

70 – 74 | 6 |

75 – 79 | 7 |

**Example:**

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.

Determine reasonable class intervals for a frequency table.

An overview of the ranked distribution, the simple frequency distribution, and the Grouped Frequency Distribution - their benefits and how to create them.

Getting averages from grouped frequency tables, including the range, mean, median and mode.

Without drawing a graph, estimate the median and quartiles and percentiles from a grouped frequency table.

Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.

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