This question has an OR — Part (a) asks to draw a histogram, frequency polygon and frequency curve for the given grouped data; Part (b) (OR) asks what classification of data means and its objectives. Both are answered in full below.

Part (a): Histogram, Frequency Polygon and Frequency Curve

Data (continuous, equal class width = 10):

Step 1 — Histogram. Since the class intervals are continuous and of equal width, a histogram is drawn by marking class limits (Marks) on the X-axis and frequency (No. of students) on the Y-axis, then erecting adjacent rectangles over each class interval with height equal to its frequency (no gaps between bars, since the classes are continuous): bars of heights 5, 12, 15, 22, 14, 4 over 0–10, 10–20, 20–30, 30–40, 40–50, 50–60 respectively.

Step 2 — Frequency Polygon. Mark the mid-points of the top of each histogram bar — these are the class mid-points (5, 15, 25, 35, 45, 55) plotted against their frequencies (5, 12, 15, 22, 14, 4). Join these mid-points with straight lines. To close the polygon, extend it to the mid-points of two imagined classes with zero frequency at each end (i.e., the class before 0–10, which is −10–0 with mid-point −5, and the class after 50–60, which is 60–70 with mid-point 65), each plotted at frequency 0, and join these to the first and last points. This can be drawn either on the same axes as the histogram (joining bar mid-tops) or independently by plotting (mid-point, frequency) pairs directly.

Frequency polygon points (mid-point, frequency): (−5, 0), (5, 5), (15, 12), (25, 15), (35, 22), (45, 14), (55, 4), (65, 0)

Step 3 — Frequency Curve. A frequency curve is obtained by smoothing the frequency polygon into a free-hand continuous curve, instead of joining the points with straight lines — the curve passes as closely as possible through (or near) all the plotted points, showing the general shape/trend of the distribution rather than its exact day-to-day fluctuation.

All three diagrams use the same X-axis (Marks, class intervals/mid-points) and Y-axis (Number of students), only the method of plotting (bars / straight-line polygon / smoothed curve) differs.

OR — Classification of Data and its Objectives

Meaning: Classification of data is the process of arranging raw, unorganised data into different groups or classes according to similarities, resemblances, or common characteristics shared by the items, so that the data becomes easier to understand and analyse.

Objectives of classification of data:

1. To condense the data — reduces a large mass of raw, scattered figures into a few meaningful, manageable groups/classes.
2. To make data simple and comprehensible — organised data is easier to read, understand and compare than raw, unsorted data.
3. To bring out similarities and dissimilarities — grouping similar items together and placing dissimilar items in different classes helps highlight patterns in the data. …