Tag: mean and median

Questions Related to mean and median

For grouped data, Arithmetic mean by Direct Method =

mean and median mean maths assumed mean method assumed mean method of finding mean measure of central tendency

  1. sfX / sf

  2. sd / N

  3. sX / N

  4. None of the above

Show answer
Correct Option: A
Explanation:

Arithmetic mean refers to the average amount in a given group of data. There are many ways to calculate arithmetic mean for grouped data like direct method where all the data are multiplied with their respective frequencies and then added up which are then divided by the summation of the frequencies or number of figures in the data in order to ascertain the mean. The formula is sfX/ sf where sfd is the summation of frequency multiplied by X for all figures and sf is the frequency or the number of element in the given data. 

For grouped data, Arithmetic mean by Assumed Mean Method =

mean and median mean maths assumed mean method assumed mean method of finding mean measure of central tendency

  1. A + sd/N

  2. A + sfd/sf

  3. sfX/sf

  4. None of these

Show answer
Correct Option: B
Explanation:

In assumed mean method, any value can be taken as assumed mean whether it is there in the data or not but it should be centrally located in the data so that to simply the big figures in the data in order to ascertain mean of the given data through easy calculations. For grouped data, the formula for assumed mean is A+ sfd/sf where A is the assumed mean, sfd is the summation of frequency multiplied with X-A for all figures and sf is the summation of frequency or the number of element in the given data. 

If 150 is divided in the ratio of 2:3:5, the distribution will be ____.

mean and median mean maths assumed mean method assumed mean method of finding mean measure of central tendency

  1. 45:55:50

  2. 50:80:20

  3. 30:45:75

  4. 50:40:60

Show answer
Correct Option: C
Explanation:

If 150 is divided in the ratio of 2:3:5, then 

= 150 * 2/10 : 150 * 3/10 : 150 * 5/10 
= 15 * 2 : 15 * 3 : 15 * 5 
= 30 : 45 : 75 

9 times of a number is equal to its square find the number_________.

mean and median mean maths assumed mean method assumed mean method of finding mean measure of central tendency

  1. 8

  2. 11

  3. 9

  4. 10

Show answer
Correct Option: C
Explanation:

Let the number in the given problem be x. Then, according to the problem 

9x = x2

=> x2 - 9x = 0

=>x ( x-9 ) =0

=> x= 0 or x= 9  

The arithmetic mean of the first 100 natural numbers is _____.

mean and median mean maths assumed mean method assumed mean method of finding mean measure of central tendency

  1. 50

  2. 52

  3. 51

  4. 50.5

Show answer
Correct Option: D
Explanation:

Arithmetic mean refers to the average amount in a given group of data. So arithmetic mean can be calculated by adding the first term and the last term of the series and then dividing the sum by 2. In the given series the first term is 1 and  the last term is 100, so the 

Arithmetic mean = ( 1+100 ) /2 
                             = 101 /2 
                             = 50.5 

The mean of a sample of size 10 is 15. If the value of each item is doubled, the mean of the sample will be _______.

mean and median mean maths assumed mean method assumed mean method of finding mean measure of central tendency

  1. 15

  2. 30

  3. 11

  4. 22

Show answer
Correct Option: B
Explanation:

Mean refers to the average amount in a given group of data. So arithmetic mean can be calculated by adding the first term and the last term of the series and then dividing the sum by 2. In the given series the first term 'a' is doubled and  the last term 'b' is also doubled , so the 

Mean = {(a+a)+ (b+b)}  /2 

          = (2a+2b) /2 

          = 2 (a+b) /2 

          = 2 [ (a+b)/2} 

Therefore, the mean is also doubled. So,if the mean was 15 then now it will be 30.  

The sum of first 10 natural numbers is____.

mean and median mean maths assumed mean method assumed mean method of finding mean measure of central tendency

  1. 100

  2. 55

  3. 50

  4. 90

Show answer
Correct Option: B
Explanation:

The series of first 10 natural numbers is an arithmetic progressions with first tern as 1 and common difference 1. So the sum of the series will be Sn = n/2 { 2a+ ( n-1 ) d } where n is the number of terms in the series, a is the first term and d is the common difference.

S10= 10/2 { 2(1) + ( 10-1 ) 1 }

     = 5 ( 2+9)

    = 5 ( 11 )

    = 55

If the frequency of observations $X _{i}$ is $f _{i} (i = 1, 2, ..... n)$.

mean and median mean maths assumed mean method assumed mean method of finding mean measure of central tendency

  1. $\overline {X} = \dfrac {X _{1}\times X _{2} \times X _{3}\times ......X _{n}}{N}$

  2. $\overline {X} = \dfrac {X _{1} + X _{2} + X _{3} + ......X _{n}}{N}$

  3. $\overline {X} = \dfrac {\sum X _{i}}{N}$

  4. $\overline {X} = \dfrac {\sum f _{i}X _{i}}{\sum f}$

Show answer
Correct Option: D

Consider following frequency distribution.

Class Intervals $0-10$ $10-20$ $20-30$ $30-40$
Frequency $8$ $10$ $12$ $15$

Arithmetic mean $=$?

mean and median mean maths assumed mean method assumed mean method of finding mean measure of central tendency

  1. $39.65$

  2. $22.55$

  3. $32.55$

  4. $23.56$

Show answer
Correct Option: B
Explanation:

0−10 | 10−20 | 20−30 | 30−40 | | --- | --- | --- | --- | --- | | Frequency(f) | 8 | 10 | 12 | 15 | | Class mark ( mid points= x) | 5 | 15 | 25 | 35 | | Fx | 40 | 150 | 300 | 525 |

Mean = summation of fx / summation of f

          = 1015/ 45

          = 22.55

The mean salary for a group of $40$ females workers is $Rs. 5,200$ per month and that for a group of $60$ male workers is $Rs. 6,800$ per month. What is the combined salary?

mean and median mean maths assumed mean method assumed mean method of finding mean measure of central tendency

  1. $6,280$

  2. $6,160$

  3. $6,890$

  4. $6,920$

Show answer
Correct Option: B
Explanation:

The mean salary of 40 females and 60 males are 5,200 and 6,800 rupees respectively. Therefore the total salary of 40 females and 60 males will be 5,200x40 and 6,800x60 rupees respectively. So the average salary of 40 females and 60 males will be

= ( 2.08,000 + 2,08,000 )/ ( 40+60)
= 616000 / 100
= 6,160