Answer
Verified
410.4k+ views
Hint – In this question use the direct formula for coefficient of variation which is ratio of standard of deviation and the mean, that is $C.V = \dfrac{{S.D}}{\mu }$, to find the standard deviation.
Complete step-by-step answer:
Given data
Mean of a distribution ($\mu $) = 4.
Coefficient of variation (C.V) = 58%.
Now as we know that coefficient of variation is the ratio of standard deviation (S.D) to mean.
Therefore, C.V = $\dfrac{{S.D}}{\mu }$
Now substitute the values we have,
$ \Rightarrow \dfrac{{58}}{{100}} = \dfrac{{S.D}}{4}$
Now simplify the above equation we have,
$ \Rightarrow S.D = \dfrac{{58 \times 4}}{{100}} = \dfrac{{58}}{{25}} = 2.32$
So this is the required answer.
Hence option (C) is correct.
Note – It’s important to understand the physical significance of standard deviation, mean and coefficient of variation. Standard deviation expresses the quantity that by how much the members of a group differ from the mean value of the group. Mean is the average of the numbers and it is defined as the ratio of summation of all the numbers divided by the total numbers. Coefficient of variation determines the greatness of the level of dispersion around the mean.
Complete step-by-step answer:
Given data
Mean of a distribution ($\mu $) = 4.
Coefficient of variation (C.V) = 58%.
Now as we know that coefficient of variation is the ratio of standard deviation (S.D) to mean.
Therefore, C.V = $\dfrac{{S.D}}{\mu }$
Now substitute the values we have,
$ \Rightarrow \dfrac{{58}}{{100}} = \dfrac{{S.D}}{4}$
Now simplify the above equation we have,
$ \Rightarrow S.D = \dfrac{{58 \times 4}}{{100}} = \dfrac{{58}}{{25}} = 2.32$
So this is the required answer.
Hence option (C) is correct.
Note – It’s important to understand the physical significance of standard deviation, mean and coefficient of variation. Standard deviation expresses the quantity that by how much the members of a group differ from the mean value of the group. Mean is the average of the numbers and it is defined as the ratio of summation of all the numbers divided by the total numbers. Coefficient of variation determines the greatness of the level of dispersion around the mean.
Recently Updated Pages
Assertion The resistivity of a semiconductor increases class 13 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE
Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE
What are the possible quantum number for the last outermost class 11 chemistry CBSE
Is C2 paramagnetic or diamagnetic class 11 chemistry CBSE
Trending doubts
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE
Which type of bond is stronger ionic or covalent class 12 chemistry CBSE
What organs are located on the left side of your body class 11 biology CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
How fast is 60 miles per hour in kilometres per ho class 10 maths CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
When people say No pun intended what does that mea class 8 english CBSE