Data Handling — Class 8

Clear notes on collection, presentation and basic statistics: frequency tables, graphs, mean, median, mode and solved examples — mobile-friendly & exam-ready.

1. Introduction to Data Handling

Data Handling (or Statistics) is the process of collecting, arranging, presenting and interpreting data. It helps us draw conclusions from numerical information and make decisions based on data patterns.

2. Types of Data

  • Primary data: Collected first-hand (e.g., survey responses).
  • Secondary data: Collected from published sources (e.g., reports).
  • Qualitative data: Descriptive (names, categories).
  • Quantitative data: Numerical (counts, measurements).
  • Discrete: Countable values (e.g., number of students).
  • Continuous: Any value in an interval (e.g., height, weight).

3. Collection & Tabulation

Raw data is organized into tables to make it easier to analyse. Frequency tables list each observation with its frequency. For grouped data, we use class intervals.

Frequency Table (example):
MarksFrequency
0–92
10–195
20–298
30–394

4. Presentation: Pictograph, Bar Graph, Histogram & Pie Chart

  • Pictograph: Uses pictures/symbols to represent data. Good for quick visualization.
  • Bar graph: For comparing categories. Bars must have equal width and gaps between them.
  • Histogram: For continuous grouped data. Adjacent bars touch; area represents frequency.
  • Pie chart: Shows proportion of each category of a whole. Angle for each sector = (frequency/total)×360°.
Graph Drawing Tips: Label axes, choose suitable scale, start axis at 0, draw neat bars/ sectors and add a clear title & legend.

5. Measures of Central Tendency

MeasureDefinition / Formula
Mean (for ungrouped)Mean = (Sum of observations) / (Number of observations)
Mean (grouped)Mean ≈ (Σ f × x) / Σ f where x is class midpoint, f is frequency.
MedianMiddle value when data ordered. For grouped data, use formula: Median = L + [(N/2 − cf) / f] × h.
ModeValue with highest frequency. For grouped data: Mode = L + [(f1 − f0)/(2f1 − f0 − f2)] × h.
RangeRange = Max − Min
(L = lower class boundary of modal class, f1 = frequency of modal class, f0 = previous class frequency, f2 = next class frequency, h = class width, cf = cumulative frequency before median class, N = total frequency.)

6. Solved Examples

Example 1 (Mean — ungrouped): Find mean of {5, 8, 12, 7, 8}.
Sum = 40, n = 5 → Mean = 40/5 = 8.
Example 2 (Mode — grouped): For class intervals 10–19(5), 20–29(12), 30–39(7) (frequencies in brackets), modal class = 20–29. Use formula to estimate mode (show steps in exam).
Example 3 (Median — grouped): Given grouped frequency table with total N = 40, median lies in class where cumulative frequency ≥ N/2. Use median formula to compute value.

7. Practice Questions (with answers)

  1. Find mean of {4, 6, 9, 11, 10}.
    Answer
    Sum = 40, n = 5 → Mean = 8
  2. Construct a bar graph for subjects: Maths(30), Science(25), English(20), Hindi(15).
    Answer
    Draw axes, choose scale, and plot bars proportional to frequencies.
  3. Find mode for data: 2,3,3,4,5,3,2.
    Answer
    Mode = 3 (highest frequency)
  4. Find range of {14, 18, 12, 9, 16}.
    Answer
    Range = 18 − 9 = 9

Show all steps clearly, especially when using grouped data formulas — partial marks are often given for intermediate calculations.