Weighted Average

Q.

Two numbers within the bracket denote the ranks of $10$ students of a class in two subjects: $(1,10),(2,9),(3,8),(4,7),(5,6),(6,5),(7,4),(8,3),(9,2),(10,1)$, then rank correlation coefficient is

1. $0$

2. $1$

3. $-1$

4. $0.5$

Q. The average weight of $25$ students of grade $7$ is $40\text{kg}$. If the weight of teacher is included, then the average weight becomes $41.5\text{kg}$. Find the weight of the teacher.

1. $81.5\text{kg}$
2. $79\text{kg}$
3. $43\text{kg}$

Q. There are $40$ students in Joe's class. In a $20$ marks class test, $10$ students got $16$ marks, $20$ students got $15$ marks and rest $10$ students got $10$ marks. The weighted average of marks in Joe's class is .

Q. If $n$ number of data points are $x_1,x_2,x_3,...,x_n$, and the corresponding weighted factors are $w_1,w_2,w_3,...,w_n$, then which of the following is incorrect?

Given notation: $n_1+n_2+n_3+...+n_l={\sum }_{i=1}^l{n}_i$

1. Average of data set= $\frac{{\sum }_{i=1}^n{x}_i}{n}$
2. Weighted average of data set= $\frac{{\sum }_{i=1}^n{w}_i{x}_i}{{\sum }_{i=1}^n{w}_i}$
3. Weighted average of data set= $\frac{{\sum }_{i=1}^n{w}_i{x}_i}{n}$

Q. The weighted average marks of $170$ students who appeared in an exam is $55$. It is also known that the average marks of failed students is $23$ and that of passed students is $63$. Find the number of students who passed the exam.

1. $34$
2. $62$
3. $106$
4. $136$

Q. The average marks of Smith and Max in a quiz is $62$. In the same quiz, the average marks of Ellen and Max is $65$ and that of Smith and Ellen is $64$. What will be the average marks of all three of them in the quiz?

1. $64$
2. $65.67$
3. $63.67$
4. $62.5$

Q. In a group, the ages (in years) of $8$ friends are $25,27,25,27,26,25,27,26$. The average age of the group is .

Q. Which of the following options are true about the weighted average?

1. The weighted average assigns certain weights to each of the individual quantities.
2. $\text{Weighted Average}=\frac{(w_1\times n_1)+(w_2\times n_2)+\dots +(w_l\times n_l)}{w_1+w_2+\dots +w_l}$,
   
   where $w_1,w_2,\dots ,w_l$ are the weighted factors and $n_1,n_2,\dots ,n_l$ are the data points.
3. Weighted average is the same as the average of the data set.
4. Assigning weights would mean different levels of importance to different quantities.
   

Q. The average resulting from the multiplication of each value by a weighted factor is known as .