Question

If the mean of the frequency distribution

Variable (\(x_i\))	1	3	4	7	9	Total
Frequency (\(f_i\))	1	\(a\)	\(b\)	3	1	10

is 5, then its variance is :

• A. \(5\)
• B. \(5.1\)
• C. \(5.2\)
• D. \(5.3\)

Hint:

Use the total frequency 10 and mean 5 to find \(a\) and \(b\), then variance \(=\frac{\sum f_ix_i^2}{10}-5^2\).

Answer 1

The Correct Option is C

Total frequency: \(1+a+b+3+1=10\Rightarrow a+b=5\).
Mean \(=5\Rightarrow \sum f_ix_i=50\): \(1+3a+4b+21+9=50\Rightarrow3a+4b=19\).
Solving with \(a+b=5\): \(b=4,\ a=1\).
\(\sum f_ix_i^2=1(1)+1(9)+4(16)+3(49)+1(81)=1+9+64+147+81=302\).
Variance \(=\dfrac{302}{10}-5^2=30.2-25=5.2\).
Answer: (3) \(5.2\)