Tag: mean and median

Questions Related to mean and median

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.

Three geometric means between 5 and 3125 are___.

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

  1. 15,75,375

  2. 25,125,625

  3. 11,44,176

  4. 10,40,160

Show answer
Correct Option: B
Explanation:

The geometric mean is a geometric series which is in the form of arn where a is the first term and r is the common ratio.

T1= 5 and T5 = 3125

Now, T1/T5 = 5/ 3125

=>ar1//ar5 =1/ 625

=> 1/ r4 = 1/625

=> r4 = 625

=> r = 5

So if r=5, then a= 1

T2 = ar2

      = 1(5) 2 = 25

T3 = ar3

      = 1(5) 3 = 125

T4 = ar4

      = 1(5)4 = 625

Therefore, three geometric means between 5 and 3125 are 25, 125 and 625. 

The most appropriate average to be used to compute the average rate of growth in population is:

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

  1. Arithmetic mean

  2. Median

  3. Geometric mean

  4. Harmonic mean

Show answer
Correct Option: C
Explanation:

In geometric mean method, the average percentage increase in the population is assumed to be constant decade to decade through which future population is worked out. Therefore, it is the most appropriate average to be used to compute the average rate of growth in population. 

The mean of a sample of size $10$ is $15$. If the value of each item is reduced by $2$, 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. $13$

  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 decreased by 2 and  the last term 'b' is also decreased by 2 , so the 

Mean = {(a-2)+ (b-2)}  /2 

          = (a+b-4) /2 

          = {(a+b)/2} - 4/2

          = {(a+b)/2} - 2 

Therefore, the mean is also decreased by 2. So,if the mean was 15 then now it will be 13. 

If the average weight of $150$ students is $60$ kg., what will be the number of boys and girls in the school if the average weight of boys and girls is $70$kg and $55$kg. respectively?

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

  1. $(50,100)$

  2. $(100,50)$

  3. $(40,110)$

  4. $(90,60)$

Show answer
Correct Option: A

Harmonic mean is a part of _______________.

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

  1. Positional average

  2. Mathematical average

  3. Both a & b

  4. None of the above

Show answer
Correct Option: B
Explanation:

Mathematical average refers to all such average where a figure is taken out through mathematical methods from the a given series that represents the whole series. Harmonic mean is a mathematical tool which is used to calculate average of a certain series. Therefore, it is a part of mathematical average. 

If the mean of x and $\displaystyle \frac{1}{x}$ is M, then the mean of x$^3$ and $\displaystyle \frac{1}{x^3}$ is

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

  1. $\displaystyle \frac{M (M^2 - 3)}{2}$

  2. $M (4M^2 - 3)$

  3. $M^3$

  4. $M^3 + 3$

Show answer
Correct Option: B
Explanation:

Given,

$M=\dfrac{x+\dfrac{1}{x}}{2}$
$2M=x+\dfrac{1}{x}$                  $ ....... (1)$

On cubing both sides, we get
$(2M)^3=(x+\dfrac{1}{x})^3$
$8M^3=x^3+\dfrac{1}{x^3}+3(x+\dfrac{1}{x})$
$8M^3=x^3+\dfrac{1}{x^3}+3(2M)$
$8M^3=x^3+\dfrac{1}{x^3}+6M$
$x^3+\dfrac{1}{x^3}=8M^3-6M$
$\dfrac{x^3+\dfrac{1}{x^3}}{2}=M(4M^2-3)$

Hence, this is the answer.