Class 6 — Mathematics (NCERT)
Data Handling: Pictographs and Bar Graphs
Class 6
- ✓Understand what data is and why it needs to be organised.
- ✓Interpret information presented in pictographs.
- ✓Draw pictographs to represent given data.
- ✓Interpret information presented in bar graphs.
- ✓Draw bar graphs to represent given data.
Key concepts
Data is a collection of facts, such as numbers, words, measurements, observations, or descriptions of things. We collect data to get information and make decisions. For example, the number of students in your class, their favourite subjects, or the marks they scored in a test are all examples of data.
Raw data, when collected, is often unorganised. To make sense of it and draw meaningful conclusions, data needs to be organised in a systematic way. Organising data helps us to quickly understand patterns and answer questions.
A pictograph is a way of representing data using pictures or symbols. Each symbol represents a certain quantity, and this quantity is specified in the 'key' or 'scale' of the pictograph. Pictographs make it easy to compare different categories of data visually.
A bar graph (or bar chart) is a visual representation of data using rectangular bars of uniform width. The length or height of each bar is proportional to the value it represents. Bar graphs can be drawn either horizontally or vertically. They are useful for comparing quantities across different categories.
Key facts to remember
- 1Data is a collection of numerical facts or information.
- 2Organising data helps in understanding and interpreting it easily.
- 3A pictograph uses pictures or symbols to represent data.
- 4Every pictograph must have a 'key' or 'scale' that tells what each symbol represents.
- 5A bar graph uses bars of uniform width to represent data.
- 6The height (or length) of each bar in a bar graph is proportional to the value it represents.
- 7Bar graphs must have properly labelled axes and a suitable scale.
- 8Both pictographs and bar graphs help in comparing different categories of data visually.
Worked examples
Example 1
The following pictograph shows the number of students present in a class during a week.\nMonday: 😃😃😃😃😃\nTuesday: 😃😃😃😃\nWednesday: 😃😃😃😃😃😃\nThursday: 😃😃😃\nFriday: 😃😃😃😃😃\nKey: 😃 = 5 students\nAnswer the following questions:\n(a) How many students were present on Wednesday?\n(b) On which day were the least number of students present?
Answer
(a) 30 students (b) Thursday
Always check the key to understand the value of each symbol.
Example 2
The number of cars sold by a dealer in five months is given below:\nMonth | Number of Cars\n----------|---------------\nJanuary | 40\nFebruary | 55\nMarch | 30\nApril | 50\nMay | 45\nRepresent the data using a pictograph.
Answer
Cars Sold by a Dealer\nMonth | Number of Cars\n----------|---------------------------------\nJanuary | 🚗🚗🚗🚗\nFebruary | 🚗🚗🚗🚗🚗🚗/2\nMarch | 🚗🚗🚗\nApril | 🚗🚗🚗🚗🚗\nMay | 🚗🚗🚗🚗🚗/2\nKey: 🚗 = 10 cars
The choice of symbol and scale is important. It should be easy to draw and represent the data clearly.
Example 3
The number of absentees in Class 6 during a week is given below:\nDay | Number of Absentees\n----------|--------------------\nMonday | 10\nTuesday | 5\nWednesday | 15\nThursday | 20\nFriday | 10\nDraw a bar graph to represent this data.
Answer
Title: Number of Absentees in Class 6\n(Imagine a graph here)\nVertical Axis (Y-axis): Number of Absentees (Scale: 1 unit = 5 absentees)\nHorizontal Axis (X-axis): Day\nBars:\n- Monday: Bar height up to 10\n- Tuesday: Bar height up to 5\n- Wednesday: Bar height up to 15\n- Thursday: Bar height up to 20\n- Friday: Bar height up to 10\nAll bars should be of uniform width and equally spaced.
Ensure the bars are of uniform width and there is equal spacing between them. The scale on the axis must be clearly marked.
Common mistakes
- ✗Not including a 'key' or 'scale' in a pictograph, making it impossible to interpret.
- ✗Using symbols that are difficult to draw or divide into fractions in a pictograph.
- ✗Not choosing an appropriate scale for the axes in a bar graph, leading to a graph that is too small or too large.
- ✗Drawing bars of unequal width or with unequal spacing between them in a bar graph.
- ✗Forgetting to label the axes or provide a title for the bar graph.
Exam tips
- ★Read the question carefully to understand what information needs to be represented or extracted.
- ★When drawing a pictograph, choose a simple symbol and a scale that allows for easy representation of all data values, including fractions if necessary.
- ★For bar graphs, always draw and label the axes clearly. Choose a scale that covers the entire range of data and makes the graph easy to read.
- ★Ensure bars in a bar graph are of uniform width and are equally spaced. Always include a title for your graph/pictograph and a key for pictographs.
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