Home » Past Questions » Mathematics » \(\begin{array}{c|c} class& 1 - 3 & 4 - 6 & 7 - 9\\ \hline Frequency & 5 & 8 & 5\end{array}\)Find the standard deviation of the data using the table above...

\(\begin{array}{c|c} class& 1 - 3 & 4 - 6 & 7 - 9\\ \hline Frequency & 5 & 8 & 5\end{array}\)Find the standard deviation of the data using the table above...


Question

\(\begin{array}{c|c} class& 1 - 3 & 4 - 6 & 7 - 9\\ \hline Frequency & 5 & 8 & 5\end{array}\)

Find the standard deviation of the data using the table above

Options

A) 5

B) \(\sqrt{6}\0

C) \(\frac{5}{3}\)

D) \(\sqrt{5}\)

The correct answer is A.

Explanation:

\(\begin{array}{c|c} \text{class intervals} & Fre(F) & \text{class-marks(x)} & Fx & (x - x)& (x - x)^2 & F(x - x)^2 \\ \hline 1 - 3 & 5 & 10 & 10 & -3 & 9 & 90\\ 4 - 6 & 8 & 40 & 40 & 0 & 0 & 0 \\ 7 - 9 & 5 & 40 & 40 & 3 & 9 & 360 \\ \hline & 18 & & 90 & & & 450 \end{array}\)
x = \(\frac{\sum fx}{\sum f}\)
= \(\frac{90}{18}\)
= 5
S.D = \(\frac{\sum f(x - x)^2}{\sum f}\)
= \(\frac{450}{18}\)
= \(\sqrt{25}\)
= 5

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Dicussion (1)

  • \(\begin{array}{c|c} \text{class intervals} & Fre(F) & \text{class-marks(x)} & Fx & (x - x)& (x - x)^2 & F(x - x)^2 \\ \hline 1 - 3 & 5 & 10 & 10 & -3 & 9 & 90\\ 4 - 6 & 8 & 40 & 40 & 0 & 0 & 0 \\ 7 - 9 & 5 & 40 & 40 & 3 & 9 & 360 \\ \hline & 18 & & 90 & & & 450 \end{array}\)
    x = \(\frac{\sum fx}{\sum f}\)
    = \(\frac{90}{18}\)
    = 5
    S.D = \(\frac{\sum f(x - x)^2}{\sum f}\)
    = \(\frac{450}{18}\)
    = \(\sqrt{25}\)
    = 5

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