Dynamics and Statistics Questions

The slope of the line touching both the parabolas y2 = 4x and x2 = - 32y is

The mean and variance of 10 observations are 9 and 34.2, respectively. If 8 of these observations are $2, 3, 5, 10, 11, 13, 15, 21$, find the mean deviation about the median of all 10 observations.

All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even aft...

Let $X = \{x \in \mathbb{N} : 1 \leq x \leq 19\}$ and for some $a, b \in \mathbb{R}$, $Y = \{ax + b : x \in X\}$. If the mean and variance of the elements of $Y$ are $30$ and $750$ respectively, then ...

The mean and variance of a dataset of 10 observations are 10 and 2, respectively. If an observation $\alpha$ in this data is replaced by $\beta$, the mean and variance become 10.1 and 1.99, respective...

The mean and variance of the data given below are $\mu$ and $19$ respectively. Find the value of $\lambda + \mu$. $$\begin{array}{|c|c|c|c|c|}\hline \text{Class} & 4-8 & 8-12 & 12-16 & 16-20 \\ \hline...

Let the mean and variance of $8$ numbers $-10,\ -7,\ -1,\ x,\ y,\ 9,\ 2,\ 16$ be $\dfrac{7}{2}$ and $\dfrac{293}{4}$, respectively. Find the mean of the $4$ numbers $x,\ y,\ x+y+1,\ |x-y|$.

If the mean deviation about the median of the numbers $k, 2k, 3k, \ldots, 1000k$ is $500$, then $k^2$ is equal to:

Mean of the first n terms of the A.P. a + (a + d) + (a + 2d) + ...... is

If median = (mode + 2 mean) M, then M is equal to-

For a normal distribution, we have

Mode of the distribution Marks 4 5 6 7 8 Number 3 5 10 6 1of students is...

The mode of the following items is 0, 1, 6, 7, 2, 3, 7, 6, 6, 2, 6, 0, 5, 6, 0 is-

The median of the items 6, 10, 4, 3, 9, 11, 22, 18 is-

In an arranged discrete series in which total number of observations ′n′ is even, median is

If a variable takes the discrete values α + 4, α −, α − , α − 3, α − 2, α + , α − , α + 5 (α > 0), then the median is-...

The median of 10, 14, 11, 9, 8, 12, 6 is

Following table shows the weight of 12 students: Weight (in kgs.) 67 70 72 73 75 No. of students 4 3 2 2 1then mean weight is-...

If first and second terms of a HP are a and b, then its nth term will be-