Class 6 Mathematics · Chapter 4 NotesData Handling and Presentation

Any collection of facts, numbers, measures, observations or other descriptions of things that convey information about those things is called data. When Navya and Naresh wanted to find the most popular game in their class, they asked every student and wrote down the answers. That list of games is data. Data is all around us — the marks of your class, the number of vehicles on a road, or the population of India in different years. Raw data is often just a long list that is hard to read at a glance. To make sense of it, we must collect it carefully and then organise it so that patterns and comparisons become visible.

• Dataa collection of facts, numbers, measures or observations that gives information
• Raw datadata in the form in which it is first collected, before organising

To answer a question like 'What is the most popular game in our class?', you first decide what to find out, then ask each person and record every response. After collecting the data, you organise it. One simple way is to arrange the values in ascending order. For example, Sushri Sandhya wrote the shoe sizes of her students on the board and then arranged them from smallest to largest: 3, 3, 3, 4, 4, ... 7. This ordered list makes it easy to see the smallest size, the largest size, and how many students wear each size. Another way is to make a frequency table, where each value is listed with the number of times it occurs.

• Ascending orderarranging data from the smallest value to the largest value
• Frequencythe number of times a particular value or observation occurs

A tally mark is a quick way to count responses while you collect them. Each response gets one mark '|', and when the count reaches five, the first four marks are crossed with a line through them, like ||||. This makes counting in fives easy. Shri Nilesh used this method when he asked children to choose their favourite sweet. He wrote the sweet names in one column, put tally marks in the next, and then wrote the total number of students in a third column. The numbers 6, 9, 13, 3 and 7 are the frequencies of jalebi, gulab jamun, gujiya, barfi and rasgulla. A table that shows values and their frequencies is called a frequency distribution table.

• Tally marks|||| represents 5
• Frequency distribution tablea table listing each value and its frequency

A pictograph represents data through pictures or symbols of objects. In a pictograph, each symbol stands for a fixed number of items, and this is called the scale or key. For example, if one symbol stands for 10 children, then 5 symbols mean 5 × 10 = 50 children, and a half symbol means 5 children. Pictographs let you compare categories at a glance. However, when the data is large or when frequencies are not exact multiples of the scale, drawing a pictograph becomes difficult. For instance, if one symbol stands for 10 students, you cannot easily show 33 or 27 students without splitting symbols awkwardly.

• Pictographa graph that uses pictures or symbols to show data
• Scale or keythe number that each symbol represents, such as one symbol = 5 students

A bar graph uses bars of uniform width drawn horizontally or vertically with equal spacing between them. The length or height of each bar shows the frequency of that category. Like pictographs, bar graphs need a scale. For example, when showing the population of India in crores, one unit length may represent 10 crores, so a bar of length 5 units means 50 crores. Bar graphs are especially useful when the data is large, because bars can be drawn accurately for any value. By looking at the longest or shortest bar, you can quickly find the maximum and minimum values, and by comparing bar heights you can compare categories.

• Bar grapha graph with equally spaced bars of equal width whose heights or lengths show frequencies
• Scalethe number that one unit length of a bar represents, such as 1 unit length = 10 runs

To draw a bar graph, first draw a horizontal line and a vertical line. Along the horizontal line, write the names of the categories with equal spacing. Along the vertical line, mark the frequencies. Choose a scale that fits the data nicely on your paper — for example, 1 unit length = 1 student for small numbers, or 1 unit length = 10 runs when scores go up to 100. Then draw bars of equal width for each category, with their heights equal to the frequency divided by the scale. The markings on the vertical axis must start from zero. Finally, give your graph a title and label the axes clearly.

• Stepsdraw axes, mark categories, choose scale, draw bars of equal width, label axes and title
• The scale markings must start from zero

Once a graph is ready, you can read it to answer questions. The longest bar shows the maximum value and the shortest bar shows the minimum. You can add frequencies to find totals, subtract to find differences, and compare bars to see which category is greater. For example, from a bar graph of traffic at a crossing, you can see that the maximum traffic was between 7 and 8 a.m. and the minimum was between 6 and 7 a.m. You can also ask why certain patterns appear — for example, why traffic was heaviest in the morning — and suggest possible reasons, which is an important part of data analysis.

• Maximumshown by the longest or tallest bar
• Minimumshown by the shortest bar
• Totalfound by adding the frequencies of the required categories

Graphs can be made more attractive with colours, pictures and creative shapes. Such decorated visual presentations are called infographics. However, artistic choices can sometimes mislead. If taller bars are also made wider, the graph suggests that taller values are also wider, which may not be true. Similarly, if a mountain is drawn twice as tall as another but also much wider, it may look more than twice as tall. While preparing or reading any graph, you must check whether the pictures accurately represent the numbers. A good graph is both visually appealing and truthful.

• Infographica data presentation that uses extensive artistic and visual imagery
• Always check that the visual size of a symbol matches the value it represents