Finding mean for Grouped Data when class Intervals are not given

Q. What is the mean proportion of 125 and 5

Q.

Find the mean of the following distribution :

$\begin{array}{cccccc}x:& 4& 6& 9& 10& 15\\ f:& 5& 10& 10& 7& 8\end{array}$

1. 7

2. 8

3. 9

4. 10

Q.

The arithmetic mean of first $n$ natural number is:

1. $\frac{(n-1)}{2}$

2. $\frac{(n+1)}{2}$

3. $\frac{n}{2}$

4. $n$

Q.

Jack made a list of shirt sizes he sold past month. He had to select only one size shirt this month so as to increase his profits. Which shirt size will he choose?

$\begin{array}{ccccc}Size& Week1& Week2& Week3& Week4\\ 90cm& 2& 3& 4& 3\\ 95cm& 5& 6& 2& 3\\ 100cm& 18& 10& 19& 13\\ 105cm& 16& 18& 14& 20\\ 110cm& 10& 8& 11& 7\\ 115cm& 1& 2& 1& 4\end{array}$

1. 90 cm
2. 100 cm
3. 105 cm
4. 110 cm

Q.

Krishna’s family has 4 members. The daily rice consumption of the 4 family members is - 0.5 kg, 0.4 kg, 0.3 kg and 0.6 kg. Krishna wants to find the average rice consumption per family member. What is the measure that will come into use now?

1. Median

2. Mean

3. Median or Mode

4. Mode

Q.

The value of ${\sum }_{i=1}^n{x}_i$ is

1. 

2. 

3. 

4. 

Q. The mean of a set of 20 observations is 19.3. The mean is reduced by 0.5 when a new observation is added to the set. The new observation is:

1. 19.8
2. 9.2
3. 8.8
4. 9.8

Q.

In a: b = b:c , a is the mean proportion between b and c . This is :

a) true

b) false

Q. The mean marks of 100 students were found to be 40. Later on, it was discovered that a score of 53 was misread as 83. Then, the correct mean will be:

1. 37.5
2. 35.6
3. 39.7
4. 38.7

Q.

If the mean of the following data is 17 then the value of p is

___

$$\begin{array}{cccccc}{x}_i& \text{10}& \text{p}& \text{18}& \text{21}& \text{25}\\ f_i& \text{10}& \text{15}& \text{7}& \text{9}& \text{9}\end{array}$$

Q.

$\sum f_i{x}_i=6Y-4$ and $\sum f_i=8$. If the mean of the distribution is 7, what is the value of Y?

1. 9
2. 10
3. 11
4. 12

Q. If the mean of $x_1$ and $x_2$ is $M_1$ and that of $x_1,x_2,x_3,x_4$ is $M_2$, then the mean of $a{x}_1,a{x}_2,\frac{x_3}{a},\frac{x_4}{a}$
is _____.

1. $\frac{M_1+M_2}{2}$
2. $\frac{a{M}_1+\left(\frac{M_2}{2}\right)}{2}$
3. $\frac{1}{2a}\left[\right(a^2-1)M_1+M_2]$
4. $\frac{1}{2a}\left[2\right(a^2-1)M_1+M_2]$

Q.

What is the mean of 70, 75, 80, 85, and 90?

1. 80

2. 70

3. 75

4. 90

Q. The distribution of height of 50 children are given. If the mean height for the distribution is 117.8 cm, then complete the following table.
$\begin{array}{ccccccc}Height& 110& 115& x_1& 120& 121& 125\\ Numberofstudents& 6& 8& 14& f_1& 4& 3\end{array}$

1. $x_1=118,f_1=15$
2. $x_1=121,f_1=15$
3. $x_1=118,f_1=8$
4. None of these

Q. Find the mean of the following observations: 20, 30, 40 and 50

1. 35
2. 20
3. 25
4. 30

Q. Each observation in a raw data is first multiplied by 3, then 6 is added. It is then divided by 3 and subsequently reduced by 6. Which of the following statements is true?

1. The new mean is equal to the original mean.
2. The new mean is 4 more than the original mean.
3. The new mean is 4 less than the original mean
4. The new mean is 2 more than the original mean

Q. If the sum of three consecutive odd numbers is 33, then what is the mean of these numbers?