Data handling is the branch of mathematics that deals with collecting, organising, representing and interpreting information. Data means facts and figures gathered from surveys, experiments, records or observations. For example, the marks of students in a test, the daily temperature of a city, the rainfall of a region or the number of students present in a school are all forms of data. In Class 7, we learn to organise raw data using tables and frequency distributions, represent it using bar graphs and double bar graphs, and summarise it using measures of central tendency such as mean, median and mode, along with the range.
The ability to handle data is used everywhere, from weather forecasting and sports statistics to business decisions and opinion polls. A good data analyst can draw conclusions quickly by computing averages and by studying how spread out the data is. This chapter builds the statistical foundation that will be extended in higher classes with pie charts, histograms, probability and more advanced measures of statistics.
Raw data collected from a survey is usually in a disorganised form. To make it useful, we organise it into a frequency distribution table. The frequency of a particular observation is the number of times it occurs in the data. For example, if we ask 20 students how many books they read in a month and get the numbers 3, 2, 5, 3, 4, 3, 2, 5, 4, 3, then the observation 3 occurs four times, so the frequency of 3 is 4. A frequency table lists each observation with its count, making the data easy to read.
When the number of observations is large and the values are spread over a wide range, we group them into intervals called class intervals or classes. For example, marks of 50 students can be grouped as 0-10, 10-20, 20-30 and so on. The lower end of an interval is the lower limit and the upper end is the upper limit. The number of observations falling in each class is its frequency.
Tally marks are used to count frequencies quickly. Each observation is recorded with a vertical stroke, and every fifth observation is marked with a diagonal stroke crossing the previous four. Groups of five tally marks make counting easy. For example, 8 observations are recorded as four strokes, one diagonal stroke and three more vertical strokes.
The arithmetic mean is the average of the data. It is found by dividing the sum of all observations by the total number of observations: Mean = Sum of all observations / Total number of observations For example, the mean of 5, 7, 8, 10, 12 is (5 + 7 + 8 + 10 + 12)/5 = 42/5 = 8.4. The mean tells us the typical value around which the data is centred.
The median is the middle value of the data when the observations are arranged in ascending or descending order. If there are an odd number of observations, the median is exactly the middle value. If there are an even number of observations, the median is the average of the two middle values. For example, for the data 4, 7, 9, 12, 15, the median is 9. For the data 4, 7, 9, 12, 15, 20, the median is (9 + 12)/2 = 10.5.
The mode is the observation that occurs the most number of times in the data. A set of data may have one mode, more than one mode, or no mode at all. For example, in the data 2, 3, 3, 3, 4, 5, the mode is 3. In the data 2, 2, 5, 5, 8, the modes are 2 and 5. If every observation occurs exactly once, the data has no mode.
The range is the difference between the highest and the lowest observation in the data: Range = Highest observation - Lowest observation For example, if the highest mark in a test is 95 and the lowest is 40, the range is 55. The range tells us how spread out or scattered the data is.
A bar graph represents data using rectangular bars of equal width. The height or length of each bar is proportional to the value it represents. Bar graphs are drawn on graph paper with a suitable scale on the vertical axis. For example, the number of students in different houses of a school can be shown with bars labelled with the house names along the horizontal axis.
A double bar graph shows two sets of data side by side for comparison. Two bars of different colours or shades are drawn for each category. For example, to compare the number of boys and girls in each class, we draw one bar for boys and one for girls for every class. A double bar graph makes comparison easy because the bars are placed next to each other.
While drawing a bar graph, the scale must be chosen carefully so that all bars fit in the graph paper and the graph is neither too small nor too large. For example, if the maximum value is 500, a scale of 1 unit = 100 makes a compact graph, while 1 unit = 10 would make very tall bars. Choose a scale such that 1 unit on the vertical axis represents a round number and the tallest bar does not exceed the height of the graph paper.
Interpreting data means drawing meaningful conclusions from the table or graph. From a frequency table we can instantly see which observation occurs most often (the mode). From a bar graph we can compare values visually, spot the largest and smallest categories, and answer questions like how much more or less one category is compared to another. Interpretation also involves the mean, median and range, which together summarise the centre and the spread of the data.
| Measure | Definition | Formula | Example |
|---|---|---|---|
| Mean | Average of all observations | Sum of observations / Number of observations | Mean of 4, 6, 8 is 6 |
| Median | Middle value in sorted data | Odd n: middle; Even n: average of two middles | Median of 3, 7, 9 is 7 |
| Mode | Most frequent observation | The value with highest frequency | Mode of 2, 2, 5 is 2 |
| Range | Spread of data | Highest - Lowest | Range of 10, 4, 8 is 6 |
| Step | Action | Remark |
|---|---|---|
| 1 | Collect and organise data into a table | Decide the categories |
| 2 | Choose a suitable scale | 1 unit = round number |
| 3 | Draw horizontal and vertical axes | Label them clearly |
| 4 | Draw bars of equal width | Height proportional to value |
| 5 | Give the graph a title | Title explains the graph |
Data handling teaches us to transform raw numbers into organised tables, informative graphs and meaningful summaries. The mean, median and mode give us the central tendency of data, while the range describes its spread. Bar graphs and double bar graphs present data visually for quick comparison and interpretation. These statistical tools are not just exam topics but essential life skills used in science, commerce, sports and media. Regular practice in organising data, choosing scales and interpreting graphs will prepare students for the more advanced statistics and probability they will meet in higher classes.