Tag: maths

Questions Related to maths

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

The average marks of three batches of students having $70, 50$ and $30$ students respectively are $50, 55$ and $45$. Find the average marks of all the $150$ students, taken together.

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

  1. $50.67$

  2. $40.67$

  3. $50.60$

  4. $40.60$

Show answer
Correct Option: A
Explanation:

The average marks of 70, 50 and 30 students respectively is 50, 55 and 45 marks. Therefore the total marks of 70, 50 and 30 students will be 70x50, 50x55, and 30x45 respectively. So the average marks of all the 150 students is 

= ( 3500 + 2750 + 1350 )/ ( 70+50+30)
= 7,600 / 150
= 50.67

Only __________ can be used for all algebraic calculations.

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

  1. mean

  2. mode

  3. median

  4. All of the above

Show answer
Correct Option: A
Explanation:

Arithmetic mean refers to the average amount in a given group of data. It is defined as the summation of all the observation in the data which is divided by the number of observations in the data. Since mean includes all the values of the series of observation therefore only this average value is included in the algebraic calculations. 

Which of the following statistics would give you the estimate of the typical examination score of a class of 35 students?

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

  1. A correlation coefficient

  2. The variance

  3. The standard deviation

  4. The mean

Show answer
Correct Option: D
Explanation:

Arithmetic mean refers to the average amount in a given group of data. There are many ways to calculate arithmetic mean like direct method where all the data are added up and then divided by the number of figures in the data in order to ascertain the mean class or assumed mean method and step deviation method, the data of the given class is reduced into smaller units which makes it easy to do calculation and ascertain the mean of the class. 

Measures of central tendency are _______________.

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

  1. inferential statistics that identify the best single value for representing a set of data

  2. descriptive statistics that identify the best single value for representing a set of data

  3. inferential statistics that identify the spread of the scores in a data set

  4. descriptive statistics that identify the spread of the scores in a data set

Show answer
Correct Option: B
Explanation:

Measures of central tendency is a mathematical concept that measures the central most value of a given series which can represent the whole set of the series. In a given series, the central location of the observation is measured through different tools in order to ascertain the most efficient value that can represent the series.