Expert Mathematics & Science Tutoring

Introduction

A histogram is a graphical representation of the frequency of data points in a given range. It's widely used in GCSE Mathematics to display and analyze statistical data. Understanding histograms is crucial for data visualization and interpretation.

Key Concepts

• Frequency: The number of data points that fall within a specific range or class interval.
• Class Interval: The range of values represented by each bar in the histogram.
• Bin: An individual bar in the histogram representing a class interval.

Step-by-Step Guide

• 1. Collect and Organize Data:

Gather your data points and determine the range (smallest to largest value).

• 2. Determine Class Intervals:

Divide the range into equal intervals, ensuring the bins are wide enough to show meaningful patterns but not too wide to lose detail.

• 3. Construct the Histogram:
• Draw the horizontal axis representing the class intervals.
• Draw the vertical axis representing the frequency.
• Create bins by drawing rectangles with widths representing the class intervals and heights representing the frequency.

Common Mistakes to Avoid

• Unequal Class Intervals: Ensure all bins represent the same range of values.
• Overlapping Data: Data points should fall within only one bin.
• Inaccurate Frequency: Count the data points correctly and represent them accurately in the histogram.

Exam Tips

• Practice drawing and interpreting histograms.
• Be familiar with the purposes and limitations of histograms.
• Pay attention to the shape of the histogram (e.g., symmetric, skewed).

Practice Problems

• 1. The following data shows the heights (in cm) of a group of students:

| Height | Frequency |

|---|---|

| 140-150 | 5 |

| 150-160 | 10 |

| 160-170 | 8 |

| 170-180 | 6 |

• a) Construct a histogram for the data.
• b) What is the modal class interval?
• 2. A survey of 100 people showed the following distribution of ages:

| Age Group | Number of People |

|---|---|

| 16-20 | 25 |

| 21-25 | 30 |

| 26-30 | 20 |

| 31-35 | 15 |

| 36-40 | 10 |

• a) Calculate the class intervals and construct a histogram.
• b) What percentage of the people are aged 26 or over?

FAQ

• Q: What if my data has a large range of values?
• A: Consider using a frequency polygon or cumulative frequency curve instead.
• Q: How can I compare different histograms?
• A: Observe the shapes, central tendency, and spread of the data in each histogram.
• Q: What is the difference between a histogram and a bar chart?
• A: A histogram is used for continuous data, while a bar chart is used for categorical data.