If there are ten values each equal to 20, then standard deviation of these values is
Answers
Answer:
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Step-by-step explanation:
answer is
Standard deviation of these values is 0 if there are ten values each equal to 10
Given:
There are ten values each equal to 10
To Find:
Standard deviation
Solution:
\overline{x} =\dfrac{\sum x_i}{N}
x
=
N
∑x
i
\sigma=\sqrt{\dfrac{\sum(x_i-\overline{x})^2}{N}
σ = SD (Standard deviation) , \overline{x}=\text{mean}
x
=mean
If all values are same then Standard deviation is 0
Hence Standard deviation is 0
Step 1:
Calculate \overline{x}=\text{mean}
x
=mean
\overline{x} =\dfrac{10+10+10+10+10+10+10+10+10+10}{10} = 10
x
=
10
10+10+10+10+10+10+10+10+10+10
=10
Step 2:
Calculate \sum(x_i-\overline{x})^2∑(x
i
−
x
)
2
x_ix
i
x_i-\overline{x}x
i
−
x
(x_i-\overline{x})^2(x
i
−
x
)
2
10 10 - 10 = 0 0
10 10 - 10 = 0 0
10 10 - 10 = 0 0
10 10 - 10 = 0 0
10 10 - 10 = 0 0
10 10 - 10 = 0 0
10 10 - 10 = 0 0
10 10 - 10 = 0 0
10 10 - 10 = 0 0
10 10 - 10 = 0 0
Sum 0
Step 3:
Calculate SD
\sigma=\sqrt{\dfrac{\sum(x_i-\overline{x})^2}{N}
\sigma=\sqrt{\dfrac{0}{10}
σ = 0
Hence, Standard deviation of these values is 0