Which statement about a frequency polygon is TRUE?

Class 9StatisticsStatistics and Probability

AIt can be drawn directly by plotting class marks against frequencies, without drawing the histogram first
BIt can only be drawn on top of a histogram
CIt is plotted using the upper limits of the classes
DIt is a bar chart whose bars have gaps

Step-by-Step Solution

A frequency polygon is the line graph of the points (class mark, frequency), so the histogram is only a convenient support and is not required. It uses class marks rather than upper limits, and it is a line graph, not a bar chart.

Answer: A) It can be drawn directly by plotting class marks against frequencies, without drawing the histogram first

Key idea: Mean of ungrouped data

**Formula**:

x

̄ = (sum of observations) / (number of observations) = Σ

x / n

.

**Example**: Marks of 5 students: 7, 8, 6, 9, 10.
Sum = 40,

n = 5

. Mean = 40/5 = 8.

**For a frequency distribution**:

x

̄ = Σ

(f

ᵢ

x

ᵢ) / Σ

f

ᵢ
Multiply each value by its frequency, sum, and divide by total frequency.

Example: marks 5, 7, 9 with frequencies 2, 3, 5.
Σ

f x = 5

·2 + 7·3 + 9·5 = 10 + 21 + 45 = 76.
Σ

f = 10

. Mean = 76 / 10 = 7.6.

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