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Some Important Point Regarding Statistics - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

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  • 36 Questions around this concept.

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In a frequency distribution, the mean and median are 21 and 22 respectively, then its mode is approximately

Which of the following is a measure of central tendency that is affected by extreme values in a dataset?

Which of the following is a statistical software program commonly used for data analysis and visualization?

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Some Important Point Regarding Statistics

Some Important Points Regarding Statistics

  1. The sum of the deviation of an observation from their mean is equal to zero. i.e. \sum^{n}_{i=1}\left ( x_i-\bar x \right )=0.
  2. The sum of the square of the deviation from the mean is minimum, i.e. \sum^{n}_{i=1}\left ( x_i-\bar x \right )^2\;\text{is least.}
  3. The mean is affected accordingly if the observations are given a mathematical treatment i.e. addition, subtraction multiplication by a constant term.
  4. If set of n1 observations has mean \bar x_1 and a set of n2 observations has mean \bar x_2, then their combined mean is \frac{n_1\bar x_1+n_2\bar x_2}{n_1+n_2}
  5. If set of  n1 observations has mean \bar x_1 and set of n2 observations has mean \bar x_2  then their combined variance is given by

            \sigma ^{2}= \frac{n_{1}\left ( \sigma _{1}^{2}+d_{1}^{2} \right )+n_{2}\left ( \sigma _{2}^{2}+d_{2}^{2} \right )}{n_{1}+n_{2}}

          where, \dpi{100} \\d_1=\bar x_1-\bar x\;\;\;\text{and}\;\;\;d_2=\bar x_ 2-\bar x 

          \\ {\sigma_{1}^{2}=\frac{1}{n_{1}} \sum_{i=1}^{n_{1}}\left(x_{1 i}-\overline{x_{1}}\right)^{2}} \\\\ {\sigma_{2}^{2}=\frac{1}{n_{2}} \sum_{j=1}^{n_{2}}\left(x_{2 j}-\overline{x_{2}}\right)^{2}}

          \bar x_1,\;\;\bar x_2 are the means and \sigma_1,\;\;\sigma_2  are the standard deviations of two series.

6. Z-Score Formula: It is a method to compare test results from a normal distribution.

For a random variable (x) from a normal distribution with mean (\mu) and standard deviation (\sigma), the Z-score can be determined by subtracting the mean from x and then dividing by the standard deviation.

\mathrm{z=\frac{(x-\mu)}{\sigma }}

Where x is a test value

\mu is the mean and 

\sigma is the standard deviation (SD).

For the average of a sample of size (n) from a population, the standard deviation is \sigma and the mean is \mu.

 

Relation between Mean, Mode and Median 

If the distribution is symmetric, the value of mean, mode and median coincide. In symmetric distribution, frequencies are symmetrically distributed on the both side of the center point of the frequency curve.

Distribution which are not symmetric is called a skewed-distribution.

The empirical relation between mean, mode and median in such distributions is: \text{Mode = 3 Median - 2 Mean.} 

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Some Important Point Regarding Statistics

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Some Important Point Regarding Statistics

Mathematics for Joint Entrance Examination JEE (Advanced) : Algebra

Page No. : 11.4

Line : 20

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