Standard Deviation of Ungrouped Data by Mean Method

Q.

The standard deviation of 20 observations is$\sqrt{5}$ If each observation is multiplied by 2, find the standard deviation and variance of the resulting observations.

Q. The amount of rainfall in a particular season for 5 days are given as 10 cm, 12 cm, 14 cm, 16 cm and 8 cm Find it's standard deviation using mean method.

1. 2.83
2. 5.25
3. 3.26
4. 4.15

Q. The number of cars sold in 5 consecutive days are given as 11, 12, 10, 8, 9. Find it's standard deviation using mean method.

1. 5.26
2. 6.45
3. 1.41
4. 3.23

Q. The number of toys sold for 5 days are given as 1, 2, 3, 4, 5.
Find it's standard deviation using mean method.

1. 2.52
2. 1.41
3. 3.25
4. 4.56

Q.

The numbers of the book bought at a book fair by 200 students from a school are given in the following table.

$\begin{array}{cccccc}No.ofbooks& 0& 1& 2& 3& 4\\ No.ofstudents& 35& 64& 68& 18& 15\end{array}$

Calculate the standard deviation.

Q. The standard deviation (S.D) of the scores 1, 2, 3, 4, 5 is:

1. 
2. 
3. 
4. 

Q.

The marks obtained by 40 students in class X of a certain school in a math paper of 100 marks total are presented in the table. Find the mean using direct method.

$$\begin{array}{cccccc}ClassInterval& 0-10& 10-20& 20-30& 30-40& 40-50\\ Numberofstudents& 3& 4& 13& 15& 5\end{array}$$

1. 28.75

Q. Calculate the mean of the following distribution using step - deviation method.
$\begin{array}{cc}\text{Class Interval}& \text{Frequency}\\ 50-55& 5\\ 55-60& 20\\ 60-65& 10\\ 65-70& 10\\ 70-75& 9\end{array}$

1. 62.3

Q. What is the class mark of class 90-120?

1. 105
2. 120
3. 90
4. 115

Q. If the median of $20,25,28,x,33,34$ is $29$, then the maximum possible value of $x$ is

1. $31$
2. $30$
3. $29$
4. $32$