Standard deviation for the following distribution is Size of Item 6 7 8 9 10 11 12 Frequency 3 6 9 13 8 5 4

NIMCET 2020 Question Paper with solutions

Question : 12 of 120

Marks: +1, -0

Standard deviation for the following distribution is

Size of Item	6	7	8	9	10	11	12
Frequency	3	6	9	13	8	5	4

Solution:

Total number of items in the distribution

=Σ f _{ i }=3+6+9+13+8+5+4=48

.
The Mean

(\ov{ x })

of the given set

=\;{∑ f _{ i } x _{ i }}/{∑ f _{ i }}

⇒ \ov{x}=\;{6 × 3+7 × 6+8 × 9+9 × 13+10 × 8+11 × 5+12 × 4}/{48}=\;{432}/{48}=9 .

Let's calculate the variance using the formula:

σ^{2}=\;{∑ x _{ i }^{2}}/{ n }-\ov{ x }^{2}

\;{∑ x _{ i }^{2}}/{ n }=\;{6^{2} × 3+7^{2} × 6+8^{2} × 9+9^{2} × 13+10^{2} × 8+11^{2} × 5+12^{2} × 4}/{48}=\;{4012}/{48}=83.58 .

∴ σ^{2}=83.58-9^{2}=83.58-81=2.58

.
And, Standard Deviation

(σ)=√{σ^{2}}=√{\;\text " Variance "\;}=√{2.58} ≈ 1 . 6 0 7

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