NTA Abhyas 2020
- Exam
- NTA Abhyas
- Year
- 2020
- Subject
- Mathematics
- Chapter
- Statistics
NTA Abhyas 2020 · Mathematics · Statistics
The mean and variance of a data set comprising 15 observations are...
The mean and variance of a data set comprising observations are and respectively. If one of the observation is deleted and two new observations and are added to the data, then the new variance of resulting data is
Options
- A
- B
- C
- D
Correct answer
B.
Step-by-step solution
Let observations are
If
{\overset{̄}{x}}_{new} = \dfrac{{x}_{1} + {x}_{2} + {x}_{3} \ldots {x}_{15} - 15 + 6 + 8}{16} = \dfrac{224}{16} = 14
\dfrac{∑ {x}_i^{2}}{15} - {\left(\overset{̄}{x}\right)}^{2} = 5⇒ {x}_{1}^{2} + {x}_{2}^{2} \ldots \ldots {x}_{14}^{2} + ( 15{)}^{2} = 230 \times 15
New variance = \dfrac{{x}_{1}^{2} + {x}_{2}^{2} \ldots \ldots {x}_{14}^{2} + {6}^{2} + {8}^{2}}{16} - {\left({\overset{̄}{x}}_{new}\right)}^{2}
If
{\overset{̄}{x}}_{new} = \dfrac{{x}_{1} + {x}_{2} + {x}_{3} \ldots {x}_{15} - 15 + 6 + 8}{16} = \dfrac{224}{16} = 14
\dfrac{∑ {x}_i^{2}}{15} - {\left(\overset{̄}{x}\right)}^{2} = 5⇒ {x}_{1}^{2} + {x}_{2}^{2} \ldots \ldots {x}_{14}^{2} + ( 15{)}^{2} = 230 \times 15
New variance = \dfrac{{x}_{1}^{2} + {x}_{2}^{2} \ldots \ldots {x}_{14}^{2} + {6}^{2} + {8}^{2}}{16} - {\left({\overset{̄}{x}}_{new}\right)}^{2}