Let the observations be x1, x2, x3, x4, x5, and x6.
It is given that mean is 8 and standard deviation is 4.
\(Mean\,\bar{x}\frac{x_1+x_2+x_3+x_4+x_5+x_6}{6}=8 …….(1)\)
If each observation is multiplied by 3 and the resulting observations are yi, then
\(y_i=3x_i,i.e,x_1=\frac{1}{3}y_i,fori=1\,to\,6\)
\(New mean,\bar{y}\frac{y_1+y_2+y_3+y_4+y_5+y_6}{6}\)
\(=\frac{(x_1+x_2+x_3+x_4+x_5+x_6)}{6}\)
\(3×8\) \( ....[(Using(1)]\)
\(=24\)
\(Standard\,deviation\,σ=√\frac{1}{n}\sum_{ti1}^6(x_i-\bar{x})^2\)
\(\sum_{i=1}^6(x_i-\bar{x})^2=96\) \( ....(2)\)
From (1) and (2), it can be observed that,
\(\bar{y}=3\bar{x}\)
\(\bar{x}=\frac{1}{3}\bar{y}\)
Substituting the values of xi and \(\bar{x}\) in (2), we obtain
\(\sum_{i=1}^6(\frac{1}{3}y_i-\frac{1}{3}\bar{y})^2=96\)
\(\sum_{i=1}^6(y_i-\bar{y})^2=864\)
Therefore, variance of new observations = \((\frac{1}{6}×864)=144\)
Hence, the standard deviation of new observations is \(√144=12\)
The variance of the following continuous frequency distribution is:
class interval | Frequency |
0 -- 4 | 2 |
4 -- 8 | 3 |
8 -- 12 | 2 |
12 -- 16 | 1 |
List-I | List-II |
---|---|
(A) Distribution of a sample leads to becoming a normal distribution | (I) Central Limit Theorem |
(B) Some subset of the entire population | (II) Hypothesis |
(C) Population mean | (III) Sample |
(D) Some assumptions about the population | (IV) Parameter |
Statistics is a field of mathematics concerned with the study of data collection, data analysis, data interpretation, data presentation, and data organization. Statistics is mainly used to acquire a better understanding of data and to focus on specific applications. Also, Statistics is the process of gathering, assessing, and summarising data in a mathematical form.
Using measures of central tendency and measures of dispersion, the descriptive technique of statistics is utilized to describe the data collected and summarise the data and its attributes.
This statistical strategy is utilized to produce conclusions from data. Inferential statistics rely on statistical tests on samples to make inferences, and it does so by discovering variations between the two groups. The p-value is calculated and differentiated to the probability of chance() = 0.05. If the p-value is less than or equivalent to, the p-value is considered statistically significant.