Arithmetic Mean

Q. The mean of 25 observations is 36. If the mean of the first 13 observations is 32 and that of the last 13 observations is 39, find the 13th observation. [4 MARKS]

Q. If a, b, c are in A.P. then b is known as arithmetic mean and it is given by $b=\frac{a+c}{2}$

1. True
2. False

Q.

If $A$ be an arithmetic mean between two numbers and $S$ be the sum of $n$ arithmetic means between the same numbers, then

1. $S=nA$

2. $A=nS$

3. $A=S$

4. None of these

Q. Question 8
The mileage (km per litre) of 50 cars of the same model was tested by a manufacturer and details are tabulated as given below
$\begin{array}{ccccc}Mileage\left(km{L}^{-1}\right)& 10-12& 12-14& 14-16& 16-18\\ Numberofcars& 7& 12& 18& 13\end{array}$
Find the mean mileage.
The manufacturer claimed that the mileage of the model was $16km{L}^{-1}.$ Do you agree with this claim?

Q. The minimum value of a data is 82 and range is 38, find the maximum value.

1. 60
2. 76
3. 82
4. 120

Q. The ages (in years) of some teachers of a school are given below.
26, 32, 38, 41, 26, 31, 35, 33, 26, 37
What is the mean age of the teachers?

1. 23.5 years
2. 32.5 years
3. 35 years
4. 38 years

Q. The mean of 10 , 12 , 18 , 13 , x , 17 is 15 find the value of x

Q.

Find the mean of the following data.

X_{i - 11 12 13 14 15 16 17 18}

_{Fi - 10 1 3 4 8 10 3 1}

_{All of Fi are corresponding to Xi}

Q.

The mean of 14, 25 , 14 , 28 , 18 , 17 , 18 , 14 , 23 , 22, 14 , 18 is ___.

1. 16

2. 17.5

3. 19.55

4. 18.75

Q.

The average of long Jump taken by an athlete is 8.05 m.

If his first 3 jumps are 8 m , 8.15 m and 8.12 m and his last jump is 7.98 m,

what will be his 4th jump distance?

1. 8.1 m

2. 7.95 m

3. 8.05 m

4. 8 m

Q.

The Mean of 5 observations is 25. If one of the observations , 27 is removed from it, what will be the new mean?

1. 24.5

2. 23.75

3. 24.25

4. 25.5

Q.

The mean of 5 observations is 12. If the mean of the first 3 observations is 10, then find the mean of the other two.

1. 10

2. 12

3. 12.5

4. 15

Q. Let p(x) = 3x³ + 4x² − 5x + 8. Find p(−2).

Q.

The given table shows the rainfall (in mm) in different cities in India for an year.

$\begin{array}{cc}\text{Cities}& \text{Rainfall (mm)}\\ \text{Delhi}& 44.6\\ \text{Mumbai}& 63.5\\ \text{Kolkata}& 60.7\\ \text{Pune}& 56.2\\ \text{Bangalore}& 60.1\\ \text{Bhubaneswar}& 49.4\\ \text{Chennai}& 61.7\\ \text{Ooty}& 56.9\\ \text{Ahmedabad}& 34.4\\ \text{Jaipur}& 32.5\end{array}$

Find the Mean rainfall (in mm) for the year.

1. 55

2. 53.5

3. 52

4. 50.25

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. What is the new observation that has been added?

1. 8.8

2. 19.8

3. 9.8

4. 9.2

Q.

The mean weight of 70 Students in a class is 60 kgs. The mean weight of boys is 70 kgs while that of girls is 50 kgs.

Find the number of boys in the class.

1. 40

2. 30

3. 35

4. 38

Q. If M is the mean of x₁, x₂, x₃, x₄, x₅ and x₆, prove that
(x₁ − M) + (x₂ − M) (x₃ − M) (x₄ − M) + (x₅ − M) + (x₆ − M) = 0.

Q.

The rainfall (in mm) in a city on $7$ days of a certain week was recorded as follows. (i) Find the range of rainfall in the above data. (ii) Find the mean rainfall for the week. (iii) On how many days was the rainfall less than the mean rainfall.

Day	Mon	Tue	Wed	Thurs	Fri	Sat	Sun
Rainfall(in mm)	$0.0$	$12.2$	$2.1$	$0.0$	$20.5$	$5.5$	$1.0$

Q. Find the mean of first 10 even natural numbers.

Q. If a and b are different positive primes such that

(i) ${\left(\frac{a^{-1}{b}^2}{a^2{b}^{-4}}\right)}^7÷\left(\frac{a^3{b}^{-5}}{a^{-2}{b}^3}\right)=a^x{b}^y$, find x and y.

(ii) ${\left(a+b\right)}^{-1}\left(a^{-1}+b^{-1}\right)=a^x{b}^y$, find x + y + 2.

Q.

Question 1
The following number of goals was scored by a team in a series of 10 matches:
2, 3, 4, 5, 0, 1, 3, 3, 4, 3
Find the mean, median and mode of these scores.

Q.

The Average number of goals scored by Manchester City football club is 2 per match.
If the Full League has 38 matches, calculate the number of goals scored by ManC exactly in the middle of the league.

1. 36

2. 40

3. 38

4. 44

Q.

The table shows the weekly profits of a fruit vendor. What is the mean profit for these weeks?

Week	1	2	3	4
Profit	$-\$125$	$-\$86$	$\$54$	$-\$35$

Q. Which of the following options is not measure for central tendency of data.

1. Mode
2. Median
3. Average
4. Mean

Q. what is the arithmetic mean of first five natural number?

Q. The average of six numbers is $3.95$. The average of two of them is $3.4$, while the average of the other two is $3.85$. What is the average of the remaining two numbers?

1. $4.6$
2. $4.5$
3. $4.7$
4. $4.8$

Q. Question 12
A total of 25 patients admitted to a hospital are tested for levels of blood sugar, (mg/dl) and the results obtained were as follows:

$\begin{array}{ccccc}87& 71& 83& 67& 85\\ 77& 69& 76& 65& 85\\ 85& 54& 70& 68& 80\\ 73& 78& 68& 85& 73\\ 81& 78& 81& 77& 75\end{array}$

Find mean, median and mode (mg/dl) of the above data.

Q. Find the mean of first 6 multiples of 3

Q.

The number of boys in a class is 30 and the number of girls is x. The mean of the number of boys and girls is 35.
If the number of girls is increased by 10 , what will be the new Mean?

1. 45

2. 40

3. 42.5

4. 35

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. 15.35

2. 15.55

3. 15.2

4. 16