Median

Q. Given the following frequency distribution with some missing frequencies
$\begin{array}{cccccccc}\text{Class}& 10-20& 20-30& 30-40& 40-50& 50-60& 60-70& 70-80\\ \text{Frequency}& 180& & 34& 180& 136& & 50\end{array}$
If the total frequency is $685$ and approximate value of median is $42.6$, then the approximate values for missing frequencies are

1. $87,23$
2. $80,25$
3. $82,24$
4. $83,22$

Q. The following data gives the distribution of height of students
$\begin{array}{cccccccc}Hight\left(incm\right)& 160& 150& 152& 161& 156& 154& 155\\ Numberofstudents& 12& 8& 4& 4& 3& 3& 7\end{array}$
The median of the distribution is

1. 155
2. 160
3. 161
4. 154

Q.

Find the mean deviation about the median for the given data.

13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17

Q.

A coaching institute has students in $3$ batches : X, Y, and Z. In a certain examination, the average marks obtained by these batches are $72,60$ and $50$ respectively. The average mark of batches X and Y taken together is $69$. If the ratio of the number of students in batches Y and Z is $6:7,$ what is the average score of all the three batches put together?

1. $59$

2. $61.6$

3. $63.5$

4. $64.7$

5. $65$

Q.

For a student to qualify for a certain course, the average of his marks in the permitted 3 attempts must be more than 60.

His first two attempts yielded only 45 and 62 marks respectively. What is the minimum score required in the third attempt to qualify?

1. 89

2. 73

3. 91

4. 83

Q.

The median of a set of 15 observations is 30.5. If each of the largest 6 observations of the set is increased by 5, then the median of the new set of observations

1. Remains the same as that of the original set.

2. Is decreased by 5

3. Is 2 times the original number

4. Is increased by 5

Q. 12, 14, 15, 04, 9, 9, 7, 7, 7, 2, 5, 7, 9, 12, 13. Find mean mode and median of this data and prove relationship between mean mode and median , mean-mode =3(mean-median)

Q.

The mean of the three numbers is $40$. All three numbers are different natural numbers. If the lowest is $19$, what could be the highest possible number of the remaining two numbers?

1. $81$

2. $40$

3. $100$

4. $71$

Q.

The mean of eight numbers is $\text{16}$. Six of the numbers are $\text{17, 10, 12, 9, 6 and 12.}$The remaining two numbers are each equal to$\text{x}$.

Find the value of $\text{x.}$

Q.

Create a set of five positive numbers (Repeats allowed) that have a median of $10$ and a mean of $14$ what thought process did you use to create your numbers? i have no clue

Q.

The mean of 10 numbers is 12.5; the mean of the first six is 15 and the last five is 10. The sixth number is

1. 15
2. 18
3. none of these
4. 12

Q. The mean and median of $100$ observations are $50$ and $52$ respectively. The value of the largest observation is $100$. It was later found that it is $110$ not $100$. Find the true mean and median.

Q. The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations in the set is
increased by 2, then the median of the new set

1. remains the same as that of the original set
2. is decreased by 2
3. is two times the original median
4. s increased by 2

Q.

Find the medians of following data sets.

Set I -- {3, 7, 2, 11, 8}

Set II -- {-1, 0, 1, 7, 11, 4}

1. 7, 2

2. 7, 2.5

3. 7.5, 2

4. 7.5, 2.5

Q. The minimum value of $f\left(x\right)=|x-6|+|x+3|+|x-8|+|x+4|+|x-3|,x\in R$ is

Q. The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations in the set is increased by 2, the median of the new set

1. increases by 2
2. decreases by 2
3. doubles
4. remains the same

Q.

Medians of following data sets are:

Set I -- {3, 7, 2, 11, 8}

Set II -- {-1, 0, 1, 7, 11, 4}

1. 7
2. 2.5
3. 7.5
4. 2

Q.

Find the lengths of the medians of the triangle with vertices A(0, 0, 6), B(0, 4, 0) and C(6, 0, 0).

Q. The mean and the median of the following ten numbers in increasing order
$10,22,26,29,34,x,42,67,70,y$
are $42$ and $35$ respectively, then $\frac{y}{x}$ is equal to :

1. $\frac{7}{2}$
2. $\frac{8}{3}$
3. $\frac{7}{3}$
4. $\frac{9}{4}$

Q. For the data : 5, 4, 8, 10, 2, 3, 5, 6, 7, 8, 10, 2, 1, 4, 6, 5, 8, 7, x, 2y, y, the median is 5 and the modes are both 5 and 2y. The value of x2 + y2 is (Consider the data to be discrete)

Q. The median of the variables $x+4,x-\frac{7}{2},x-\frac{5}{2},x-3,x-2,x+\frac{1}{2}$$x-\frac{1}{2},x+5(x>0)$, is

1. $x-3$
2. $x-2$
3. $x+\frac{5}{4}$
4. $x-\frac{5}{4}$

Q.

The sum and sum of squares corresponding to length x (in cm) and weight y

(in gm) of 50 plant products are given below:

Which is more varying, the length or weight?

Q. let a, b, c be three numbers with mean=0, median=0 and s†an dard deviation =1 Then(a, b, c) is

Q.

The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new set

1. Remains the same as that of the original set

2. Is increased by 2

3. Is two times the original median.

4. Is two times the original median.

Q.

The median of a set of 15 observations is 30.5. If each of the largest 6 observations of the set is increased by 5, then the median of the new set of observations

1. Is 2 times the original number

2. Is increased by 5

3. Is decreased by 5

4. Remains the same as that of the original set.

Q.

The mean of the first five prime numbers is

1. $5.6$

2. $7.8$

3. $39$

4. $41$

Q. The median of the variables $x+4,x-\frac{7}{2},x-\frac{5}{2},x-3,x-2,x+\frac{1}{2}$$x-\frac{1}{2},x+5(x>0)$, is

1. $x-3$
2. $x-2$
3. $x+\frac{5}{4}$
4. $x-\frac{5}{4}$

Q.

The sum and sum of squares corresponding to length x (in cm) and weight y

(in gm) of 50 plant products are given below:

Which is more varying, the length or weight?

Q. $\mathrm{Given}a\mathrm{data}\mathrm{set}\mathrm{consisting}\mathrm{of}\mathrm{just}2\mathrm{observations}\left(\mathrm{each}\mathrm{occuring}\mathrm{once}\right),\mathrm{what}\mathrm{is}\mathrm{true}\mathrm{for}\mathrm{the}\mathrm{given}\mathrm{data}\mathrm{set}?$

1. Mean and median is same.
2. Mean and mode is same.
3. Median and mode is same.
4. No relation can be determined.