The marks obtained by 10 students in a Statistics test are 24, 47, 18, 32, 19, 15, 21, 35, 50 and 41.
Understanding the Problem
The question asks us to calculate the Mean Deviation for the largest five observations from a given set of marks obtained by 10 students in a Statistics test. The marks are: 24, 47, 18, 32, 19, 15, 21, 35, 50, and 41.
Identifying the Largest Five Observations
First, we need to identify the largest five observations from the list. To do this, we should arrange the marks in ascending order:
15, 18, 19, 21, 24, 32, 35, 41, 47, 50
From the sorted list, the largest five observations are:
32, 35, 41, 47, 50
Calculating the Mean of the Largest Five Observations
Next, we calculate the mean (average) of these five observations. Let's denote these observations as \(x_1, x_2, x_3, x_4, x_5\).
The mean (\(\bar{x}\)) is calculated using the formula:
\(\bar{x} = \frac{\sum_{i=1}^{5} x_i}{5}\)Substituting the values:
\(\bar{x} = \frac{32 + 35 + 41 + 47 + 50}{5}\) \(\bar{x} = \frac{205}{5}\) \(\bar{x} = 41\)So, the mean of the largest five observations is 41.
Calculating Mean Deviation
The Mean Deviation (MD) is the average of the absolute differences between each observation and the mean.
The formula for Mean Deviation is:
\(MD = \frac{\sum_{i=1}^{5} |x_i - \bar{x}|}{5}\)Now, we calculate the absolute difference of each of the largest five observations from their mean (which is 41):
- \(|32 - 41| = |-9| = 9\)
- \(|35 - 41| = |-6| = 6\)
- \(|41 - 41| = |0| = 0\)
- \(|47 - 41| = |6| = 6\)
- \(|50 - 41| = |9| = 9\)
Finally, we calculate the Mean Deviation by averaging these absolute differences:
\(MD = \frac{9 + 6 + 0 + 6 + 9}{5}\) \(MD = \frac{30}{5}\) \(MD = 6\)Conclusion
The Mean Deviation of the largest five observations (32, 35, 41, 47, 50) from the given dataset is 6.
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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
