The given data is
13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17.
Here, the numbers of observations are 12, which is even.
Arranging the data in ascending order, we obtain
10, 11, 11, 12, 13, 13, 14, 16, 16, 17, 17, 18
Median,M=\(\frac{(\frac{12}{2})^{th}observation+(\frac{12}{2}+1)^{th} \text{observation}}{2}\)
= \(\frac{6^{th}observation +7^{th} observation}{2}\)
=\(\frac{13+14}{4}=\frac{27}{2}=13.5\)
The deviations of the respective observations from the median, i.e. \(x_i-M,\) are
3.5, 2.5, 2.5, 1.5, 0.5, 0.5, 0.5, 2.5, 2.5, 3.5, 3.5, 4.5
The absolute values of the deviations, \(|x_i-M|,\) are
3.5, 2.5, 2.5, 1.5, 0.5, 0.5, 0.5, 2.5, 2.5, 3.5, 3.5, 4.5
The required mean deviation about the median is
M.D.(M)= \(\frac{\sum_{I=1}^{12}|x_i-M|}{12}\)
=\(\frac{3.5+2.5+ 2.5+1.5+0.5+0.5+0.5+ 2.5+ 2.5+ 3.5+ 3.5+4.5}{12}\)
=\(\frac{28}{12}=2.33\)
Class | 0 – 15 | 15 – 30 | 30 – 45 | 45 – 60 | 60 – 75 | 75 – 90 |
---|---|---|---|---|---|---|
Frequency | 11 | 8 | 15 | 7 | 10 | 9 |
Variance of the following discrete frequency distribution is:
\[ \begin{array}{|c|c|c|c|c|c|} \hline \text{Class Interval} & 0-2 & 2-4 & 4-6 & 6-8 & 8-10 \\ \hline \text{Frequency (}f_i\text{)} & 2 & 3 & 5 & 3 & 2 \\ \hline \end{array} \]
Give reasons for the following.
(i) King Tut’s body has been subjected to repeated scrutiny.
(ii) Howard Carter’s investigation was resented.
(iii) Carter had to chisel away the solidified resins to raise the king’s remains.
(iv) Tut’s body was buried along with gilded treasures.
(v) The boy king changed his name from Tutankhaten to Tutankhamun.
Find the mean deviation about the median for the data
xi | 15 | 21 | 27 | 30 | 35 |
fi | 3 | 5 | 6 | 7 | 8 |
A statistical measure that is used to calculate the average deviation from the mean value of the given data set is called the mean deviation.
The mean deviation for the given data set is calculated as:
Mean Deviation = [Σ |X – µ|]/N
Where,
Grouping of data is very much possible in two ways: