Standard Deviation of Ungrouped Data by Direct Method

Q. The number of televisions sold in each day of a week are 13, 8, 4, 9, 7, 12, 10. Find it's standard deviation by direct method.

1. 2.83
2. 3.87
3. 4.52
4. 6.35

Q. For observations $x_1,x_2,x_3,..........,x_n,$ if ${\sum }_{i=1}^n(x_i+1{)}^2=9n$ and ${\sum }_{i=1}^n(x_i-1{)}^2=5n.$, then standard deviation of the data is

1. $\sqrt{3}$
2. $\sqrt{5}$
3. $\sqrt{2}$
4. $\sqrt{10}$

Q. Find the variance and standard deviation of the wages of 9 workers given below: ₹310, ₹290, ₹320, ₹280, ₹300, ₹290, ₹320, ₹310, ₹280.
$\left[4\right]$

Q. The number of cars manufactured in each day of a week are 2, 4, 6, 8, 10, 5, 7. Find the standard deviation of the number of cars manufactured using Direct method.

1. 2.83
2. 3.45
3. 6.35
4. 8.23

Q. The number of refrigerators sold in 5 consecutive days are 4, 5, 9, 10, 12. Find the standard deviation of the number of refrigerators sold using Direct method.

1. 3.03
2. 4.21
3. 6.32
4. 4.56

Q. The number of refrigerators sold in 5 consecutive days are 4, 5, 9, 10, 12. Find the standard deviation of the number of refrigerators sold using Direct method.

1. 3.03
2. 6.32
3. 4.56
4. 4.21

Q. The number of cars manufactured in each day of a week are 2, 4, 6, 8, 10, 5, 7. Find the standard deviation of the number of cars manufactured using Direct method.

1. 2.83
2. 3.45
3. 6.35
4. 8.23

Q. Mode of the data 15, 14, 19, 20, 15, 18, 14, 19, 15, 17, 15 is:

1. 16
2. 15
3. 17
4. 14

Q. The number of bridges constructed in 5 consecutive months are 1, 2, 3, 4, 5. Find the Standard deviation of the number of bridges constructed using Direct method.

1. 1.41
2. 2.14
3. 3.21
4. 4.28

Q.

Let $S$ be the standard deviation of $n$ observations. Each of the $n$ observations is multiplied by a constant $C$. Then the standard deviation of the resulting number is

1. CS

2. $S\sqrt{C}$

3. none of these

4. S

Q. The number of bridges constructed in 5 consecutive months are 1, 2, 3, 4, 5. Find the Standard deviation of the number of bridges constructed using Direct method.

1. 2.14
2. 1.41
3. 3.21
4. 4.28

Q. Deviation = Class mark - assumed mean

1. True
2. False

Q. The mean of the given data is .

$\begin{array}{cc}x& f\\ 4& 10\\ 8& 11\\ 12& 9\\ 16& 13\end{array}$

1. 10.33
2. 10
3. 10.5

Q. A class mark is a mid-point of the class interval.

1. True
2. False

Q.

Calculate the Mean of the given distribution, using Assumed mean Method.

$\begin{array}{cc}\text{Marks}& \text{No. of Students}\\ 10-20& 2\\ 20-30& 6\\ 30-40& 10\\ 40-50& 12\\ 50-60& 9\\ 60-70& 8\\ 70-80& 4\\ 80-90& 3\end{array}$

1. 48.89

Q. Median of the numbers 3, 4, 5, 6, 7 is:

1. 5
2. 7
3. 4
4. 6

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.

1. 2√5, 20

2. 5√5, 30

3. 5√5, 20

4. 2√5, 30