13656
Summation Calculation from Mean
This solution details the calculation for a summation expression, using the provided mean of observations.
Step 1: Calculate Sum of Observations
We are given 20 observations (\(x_1, \dots, x_{20}\)) with a mean \(\bar{x}=1.414\). The mean formula is \( \bar{x} = \frac{\sum_{i=1}^{n} x_i}{n} \).
Using the given values (\(n=20\)):
\( \sum_{i=1}^{20} x_i = n \times \bar{x} = 20 \times 1.414 = 28.28 \)Step 2: Evaluate the Summation Expression
We need to find the value of \(\sum_{i=1}^{20} 100(2x_i + 4)\). We apply summation properties:
1. Factor out the constant 100:
\( 100 \sum_{i=1}^{20} (2x_i + 4) \)2. Split the summation and simplify:
\( 100 \left( \sum_{i=1}^{20} 2x_i + \sum_{i=1}^{20} 4 \right) \)3. Use the sum of \(x_i\) and the sum of a constant (\( \sum_{i=1}^{n} c = n \times c \)):
\( 100 \left( 2 \sum_{i=1}^{20} x_i + (20 \times 4) \right) \)4. Substitute the calculated sum \(\sum_{i=1}^{20} x_i = 28.28\) and calculate:
\( 100 \left( 2 \times 28.28 + 80 \right) \) \( = 100 \left( 56.56 + 80 \right) \) = 100 (136.56) = 13656Final Answer
The calculated value of the summation is 13656.
Similar Questions
- What is the value of \(n\) ?
- What is the mean of the distribution ?
- What is the value of \(p + q\) ?
- What is \(\sum_{i=1}^n x_i f_i\) equal to ?
- A bag contains 5 black and 4 white balls. A man selects two balls at random. What is the probability that both of these are of the same colour?
- What is the mean deviation of the largest five observations ?
- What is the variance of the largest five observations ?
What is the median height of the class?
What is the total number of students whose height is less than or equal to 165 cm?
The height which occurs most frequently in the class is
Important Questions from Statistics
- Match the LIST-I with LIST-II
LIST-I LIST-II A. Sampling error I. Values that describe the characteristics of a population B. Parameters II. The standard deviation of the sampling distribution C. Sampling fraction III. Variation among sample statistics due to change D. Standard error IV. Proportion of the population contained in a sample
Choose the correct answer from the options given below: Given below are two statements one is labelled as Assertion (A) and the other is labelled as
Reason (R).
Assertion (A): Additive model considers the total of various components resulting in the given
values of the over all time series and it is stated as:
$Y=T+C+S+I$
Reason (R): Multiplicative model assumes that the various components interact in a
multiplicative manner to produce the given values of the over all time series and
can be stated as $Y=T \times C \times S \times I$
In the light of the above statements, choose the most appropriate answer from the options given
below:
Match List - I with List - II.
List - I List - II A. Sample proportion P = x/n I. $\frac{\sigma}{\sqrt{n}}$ B. Sample variance $S_1^2 = \frac{1}{n-1} \sum_{i=1}^{n}(xi-x̄)^2$ II. $\sigma^2 \sqrt{\frac{2}{n}}$ C. Sample variance $S^2 = \frac{1}{n} \sum_{i=1}^{n}(xi-x̄)^2$ III. $\sigma^2 \sqrt{\frac{2}{(n-1)}}$ D. Sample mean $\bar{x} = \frac{1}{n} \sum_{i=1}^{n}xi$ IV. $\sqrt{\frac{\pi(1-\pi)}{n}}$
Choose the correct answer from the options given below :- The measurement or determinations of length, height, weight, volume, area, pressure etc. comes under:
- Which of the following options explain what a 'mean' assumes ?
(i) an interval level of measurement
(ii) a nominal level of measurement
(iii) an ordinal level of measurement
(iv) a ratio level of measurement
