Dr Frost GCSE Histograms Objectives To understand why

ζ Dr Frost GCSE - Histograms Objectives: To understand why a histogram is useful for displaying data, and how to both draw and interpret a histogram.

Age (years) Frequency 15 ≤ a < 20 15 20 ≤ a < 50 15 Pablo is hosting a party. He counts how many people are between 15 and 20, and 20 and 50. Why is below graph somewhat unhelpful. How could we fix it? Frequency Click to Start Bromanimation 15 10 20 30 Age 40 50

Age (years) Frequency 15 ≤ a < 20 15 20 ≤ a < 50 15 Let’s presume that within each age group, the ages are evenly spread. Then there would ? 3 people of each age in the 15 -20 group, and 0. 5 ? people of each age in the 20 -50 group. Click to Start Bromanimation Frequency Density Estimated Frequency 3 The resulting diagram is known as a histogram. The ‘frequency per age’ is known as the ‘frequency density’. In general, given the frequency and class width, we can calculate it using: Frequency Density = Class ? Width 2 1 10 20 30 Age 40 50

Bar Charts vs Histograms Bar Charts • For discrete ? data. • Frequency given by height ? of bars. Frequency Density • For continuous ? data. • Data divided into (potentially uneven) intervals. • Frequency given by area ? of bars. 6 7 8 Shoe Size 9 1. 0 m 1. 2 m 1. 4 m 1. 6 m 1. 8 m Height

Copy and complete Weight (w kg) Frequency Density 0 < w ≤ 10 40 4 10 < w ≤ 15 6 1. 2 15 < w ≤ 35 52 35 < w ≤ 45 10 Frequency = 15? Frequency Density 5 ? ? Freq 2. 6 F. D. 1 Frequency = 40? Frequency = 25? 4 3 Frequency = 30 ? 2 1 10 20 Width 30 Height (m) 40 50

Frequency Density ? 4. 2 (using ? graph) 6 (using? graph) 40 20 ? =2 18 30 ? = 0. 6 Start by adding a Frequency Density column 30 = 1 ? 60 ? 84 8 7 6 5 4 The Box of Helpfulness We don’t know the scale on the frequency density axis. Can we work it out using the first row of the table? 3 2 Freq 1 F. D. Width This triangle will help throughout.

Determining the frequency density scale 3 ? 2 1 0 10 20 16 Frequency Density 4 Frequency Density Copy the diagram and table, then work out the scale on the frequency density axis. 12 ? 8 4 0 10 20 2 ? 1 20 Height (m) Frequency 28 36

Exercises Provided collection of past GCSE questions.

In pairs, work out the following… ?

Summary Tips you might give your classmates. . . Purpose: Histograms allow us to display continuous data ? grouped into (potentially non-fixed) intervals. Frequency Density Formula: Frequency Density is ‘frequency per unit value’, i. e: Freq ? F. D. Width Area: The area of a bar is equal to the frequency*. ? * Actually it’s only proportional to it, but you don’t need to worry about that till A Level. Working out the F. D. scale: If the frequency is known and the bar height is known, we ? can work out the scale using the formula on the left. Working out proportion of things (no FD scale given): Use any arbitrary scale for FD axis. Use it to find area of region ? that matches description. Divide by total area.