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.
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 variance of the largest five observations ?
What is the total number of students whose height is less than or equal to 165 cm?
What is the median height of the class?
The height which occurs most frequently in the class is
The most appropriate graphical representation of the given frequency distribution is
Important Questions from Statistics
Match the following:
(a) Marginalist Revolution (i) Samuelson (b) Multiplier-Accelerator model (ii) J. R. Hicks (c) IS-LM curves (iii) Jevous (d) Real Business Cycle (iv) Robert J. Borro Choose the correct option from those given below:
As per the SRS Bulletin of September 2017, the estimated death rate for Kerala is 7.6, while for Bihar it is 6. From these data which is the correct inference to draw?
Arrange the following States in descending order according to Maternal Mortality Ratio (MMR) as per the Special Bulletin of SRS, May, 2018:
(i) Assam
(ii) Bihar
(iii) Madhya Pradesh
(iv) Uttar Pradesh
Choose the correct answer from the code given below :
Which of the following statements is true for the Indian economy according to the World Bank figures for 2017?
Harrod's Growth model is given as under:
\(\begin{array}{ll} \mathrm{S}_{\mathrm{t}}=\alpha \mathrm{Y}_{\mathrm{t}} & 0<\alpha<1 \\ \mathrm{I}_{\mathrm{t}}=\beta\left[\mathrm{Y}_{\mathrm{t}}-\mathrm{Y}_{\mathrm{t}-1}\right] & \beta>0 \\ \mathrm{~S}_{\mathrm{t}}=\mathrm{I}_{\mathrm{t}} & \end{array}\)
where S t = Savings, Y t = Income, l t = Investment, t = time
In this model for economic growth, the condition for economic growth is
