Arithmetic Mean from Frequency Table

Q. The production of soyabean per acre, in quintal obtained by 27 farmers in Raipur, is given below:

9, 6, 7, 7, 5, 4.5, 8.5, 4, 5, 4, 9, 9, 8.5, 7, 7, 7, 6, 5, 5, 5, 5, 4.5, 4.5, 4.5, 4, 4, 4

From the given data, prepare a frequency table and find the average production per acre of soyabean.

1. 5.1 quintal
2. 5.2 quintal
3. 5.0 quintal
4. 5.9 quintal

Q. Calculate the arithmetic mean of the following frequency table.

$\begin{array}{cc}{x}_i& f_i\\ 1& 20\\ 2& 5\\ 3& 15\\ 4& 5\end{array}$

1. 3.11
2. 2
3. 2.11
4. 3

Q. $\sum f_i$ and $\sum f_i{x}_i$ of the given data are respectively_____ and ______.
$\begin{array}{cc}\text{Number of runs}\left(x_i\right)& \text{Tally marks}\\ 1& |||\\ 2& ||||||\\ 4& |\\ 6& ||||\end{array}$

1. 20, 50
2. 45, 15
3. 15, 45
4. 10, 25

Q. The mean of the following frequency table is 10. Find the value of a.

$x_i$	$f_i$
10	10
12	5
14	a
15	2
5	8

1. 
   10
2. 
   7
3. 
   8
4. 
   5

Q. $\sum$ (sigma) indicates the ____.

1. sum
2. subtraction
3. multiplication
4. division

Q.

1. 3.2
2. 3.3
3. 3.4
4. 3.1

Q. The marks obtained by 22 students of std 8 in a test of 80 marks are given below. Find the mean of the data.

1. 54.22
2. 54.23
3. 54
4. 54.11

Q. If values of x of the following frequency table is increased by 1 then what happens to its mean?

x	f
1	6
2	4
3	2
4	5
5	3

1. It is increased by 1
2. It is decreased by 1
3. It is doubled
4. It stays the same

Q. Find the value of $\sum f_i{x}_i$ when the mean = 6 and N = 9.

1. 44
2. 40
3. 42
4. 54

Q. The following table shows the monthly income of 20 families. How many families have Rs 50000 as their monthly income.

Monthly income(Rs)	Number of families(frequency)
20, 000	2
50, 000	4
1, 00, 000	5
75, 000	6
60, 000	3

1. 
   5
2. 
   4
3. 
   2
4. 
   3

Q. The number of members in the 22 families in Bhilar are as follows:
1, 1, 2, 2, 4, 1, 1, 1, 2, 2, 2, 2, 3, 4, 3, 3, 3, 5, 5, 6, 7, 6. Prepare the frequency table.

1. 
2. 
3. 
4. 

Q. The following table shows the monthly income of 20 families.Find the mean monthly income of those families.

Monthly income ($x_i$)	Number of families ($f_i$)	$f_i{x}_i$
20000	2	40000
50000	4	200000
100000	5	500000
75000	6	450000
60000	3	180000

Q.

The mean of the following distribution is:

$\begin{array}{ccccc}{x}_i& 10& 13& 16& 19\\ f_i& 2& 5& 7& 6\end{array}$

1. 15.2

2. 15.35

3. 15.55

4. 16

Q. The sum of the frequencies of the runs 2 and 6 is _____.
$\begin{array}{cccc}\text{Number of runs}\left(x_i\right)& \text{Tally marks}& \text{Frequency}\left(f_i\right)& f_i{x}_i\\ 1& |||& 3& 3\\ 2& ||||||& 7& 14\\ 4& |& 1& 4\\ 6& ||||& 4& 24\end{array}$

1. 11
2. 7
3. 15
4. 10

Q.

Find the missing number.

$\frac{10}{18}=\frac{?}{27}$

Q.

Find the missing number.

$11˸?\colon\colon 44˸12$

Q.
Find the value of mean.

1. 6.5
2. 6.2
3. 6.3
4. 6.1

Q.

The average value of a group of observations is 25. If the observations are 29, 32, 16, 7, x and x+4, then find the value of x.

1. 31

2. 53

3. 21

4. 43

Q.

1. 4.5
2. 4.6
3. 4.1
4. 4.2

Q.

1. 5
2. 5.2
3. 5.3
4. 5.1

Q. The following table shows the monthly income of 20 families.Find the mean monthly income of those families.

Monthly income ($x_i$)	Number of families ($f_i$)	$f_i{x}_i$
20000	2	40000
50000	4	200000
100000	5	500000
75000	6	450000
60000	3	180000

Q. Consider the following frequency distribution; Monthy income in Rs

More than or equal to 10000
More than or equal to 13000
More than or equal to 16000
More than or equal to 19000
More than or equal to 22000
More than or equal to 25000 No of families

100
85
69
50
33
15
Find the number of families having income range from Rs 16000 to Rs 19000

Q.

Find the missing number.

$44˸?\colon\colon 11˸6$

Q. The mean of the following frequency table is 10. Find the value of a.

$x_i$	$f_i$
10	10
12	5
14	a
15	2
5	8

(2 marks)

Q.

Find the missing number.

$35˸45\colon\colon ?˸9$

Q. The weekly pocket expenses (in rupees) of 30 students of a class are given below:
62, 80, 110, 75, 84, 73, 60, 62, 100, 87, 78, 94, 117, 86, 65, 68, 90, 80, 118, 72, 95, 72, 103, 96, 64, 94, 87, 85, 105, 115.
Construct a frequency table with class intervals 60−70 (where 70 is not included), 70−80, 80−90, etc.

Q.

Find the missing number.

$6˸24\colon\colon ?˸4$

Q.

Find the missing number

$\frac{10}{18}=\frac{n}{27}$

Q. What is the average of $\frac{1}{3}$ and $\frac{1}{6}$?

1. $\frac{1}{4}$
2. $\frac{2}{9}$
3. $\frac{2}{3}$
4. $\frac{1}{9}$

Q. The total score made by the men of groups $G_1$ and $G_3$ is

1. 45
2. 60
3. 55
4. 50