Median

Q.

Why is the central limit theorem so important to the study of sampling distributions group of answer choices?

Q.

What is the central limit theorem and why is it important?

Q. The mean and median of a distribution are 22.5 and 20 respectively. The mode is approximately .

1. 20
2. 12
3. 15
4. 5

Q.

The harmonic mean of $\frac{\mathrm{a}}{1-\mathrm{ab}}$ and $\frac{\mathrm{a}}{1+\mathrm{ab}}$ is

1. $\frac{\mathrm{a}}{\sqrt{1-{\mathrm{a}}^2{\mathrm{b}}^2}}$

2. $\frac{\mathrm{a}}{1-{\mathrm{a}}^2{\mathrm{b}}^2}$

3. $\mathrm{a}$

4. $\frac{1}{1-\mathrm{ab}}$

Q.

What does the central limit theorem require?

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 average of $5$ distinct positive integers is $33$. If the average of the three largest numbers within this set is $39$ then the difference of the maximum and minimum possible values of the median of the $5$ numbers is

1. $12$
2. $14$
3. $8$
4. $9$

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.

Q. If the mean of the set of number $x_1,x_2...x_n$ is $\overline{x}$ , then the mean of the number $x_i+2i,1\le \le n$ is

1. $\overline{x}+2n$
2. $\overline{x}+n+1$
3. $\overline{x}+2$
4. $\overline{x}+n$

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. For the odd numbers between $8$ and $24$, the correct option(s) is/are

1. Median is $15$
2. Median is $16$
3. Mean is $15$
4. Mean is $16$

Q. Find the median of the following data:
$$\begin{array}{cc}\text{Value}& \text{Frequency}\\ 23& 2\\ 45& 3\\ 49& 5\\ 53& 16\\ 60& 14\\ 67& 13\\ 70& 7\end{array}$$

1. 53
2. 60
3. 49
4. 51

Q.

$A,B,C$ are three sets of values of $x$:

$$\begin{gathered} A:2,3,7,1,3,2,3 \\ B:7,5,9,12,5,3,8 \\ C:4,4,11,7,2,3,4 \end{gathered}$$

Which of the following statements is correct?

1. Mean of A= Mode of C

2. Mean of C= Median of B

3. Median of B= Mode of A

4. Mean, Median and Mode of A are equal.

Q. For the proper divisors of $360$, the correct option(s) is/are

1. mean is $35.21$
2. mean is $26.78$
3. median is $18$
4. median is $19$

Q. Find the median of the following data:
$$\begin{array}{cc}\text{Value}& \text{Frequency}\\ 23& 2\\ 45& 3\\ 49& 5\\ 53& 16\\ 60& 14\\ 67& 13\\ 70& 7\end{array}$$

1. 53
2. 60
3. 49
4. 51