Certainly! Let's tackle each part step-by-step.
### Part (a): Finding the Medians of Different Sets of Data
(i) Data Set: 18, 16, 27, 20, 25
1. Arrange the data in ascending order: [tex]\( 16, 18, 20, 25, 27 \)[/tex]
2. The number of data points is 5, which is odd, so the median is the middle number.
3. The median is [tex]\( 20 \)[/tex].
(ii) Data Set: 21, 28, 14, 42, 35
1. Arrange the data in ascending order: [tex]\( 14, 21, 28, 35, 42 \)[/tex]
2. The number of data points is 5, which is odd, so the median is the middle number.
3. The median is [tex]\( 28 \)[/tex].
(iii) Data Set: 15, 30, 35, 25, 20, 45, 40
1. Arrange the data in ascending order: [tex]\( 15, 20, 25, 30, 35, 40, 45 \)[/tex]
2. The number of data points is 7, which is odd, so the median is the middle number.
3. The median is [tex]\( 30 \)[/tex].
(iv) Data Set: 22, 16, 14, 26, 32, 30
1. Arrange the data in ascending order: [tex]\( 14, 16, 22, 26, 30, 32 \)[/tex]
2. The number of data points is 6, which is even, so the median is the average of the two middle numbers.
3. The median is [tex]\( \frac{22 + 26}{2} = \frac{48}{2} = 24.0 \)[/tex].
(v) Data Set: 16, 13, 10, 14, 11, 12, 15
1. Arrange the data in ascending order: [tex]\( 10, 11, 12, 13, 14, 15, 16 \)[/tex]
2. The number of data points is 7, which is odd, so the median is the middle number.
3. The median is [tex]\( 13 \)[/tex].
### Part (b): Finding the Median Weight
Weights: 50 kg, 54 kg, 45 kg, 63 kg, 48 kg
1. Arrange the weights in ascending order: [tex]\( 45, 48, 50, 54, 63 \)[/tex]
2. The number of data points is 5, which is odd, so the median is the middle number.
3. The median weight is [tex]\( 50 \)[/tex] kg.
### Part (c): Finding the Median Age
Ages: 47, 61, 13, 34, 56, 22, 8
1. Arrange the ages in ascending order: [tex]\( 8, 13, 22, 34, 47, 56, 61 \)[/tex]
2. The number of data points is 7, which is odd, so the median is the middle number.
3. The median age is [tex]\( 34 \)[/tex].
### Part (d): Finding the Position of the Median Marks
Given table of marks:
\begin{tabular}{|l|c|c|c|c|c|}
\hline
Marks & 18 & 27 & 32 & 40 & 46 \\
\hline
No. of students & 2 & 3 & 10 & 9 & 5 \\
\hline
\end{tabular}
1. Determine the total number of students: [tex]\( 2 + 3 + 10 + 9 + 5 = 29 \)[/tex]
2. The position of the median is given by [tex]\( \frac{N + 1}{2} \)[/tex] where [tex]\( N \)[/tex] is the total number of students.
3. Hence, the position of the median is [tex]\( \frac{29 + 1}{2} = \frac{30}{2} = 15 \)[/tex].
### Summary
1. Median (i): [tex]\( 20 \)[/tex]
2. Median (ii): [tex]\( 28 \)[/tex]
3. Median (iii): [tex]\( 30 \)[/tex]
4. Median (iv): [tex]\( 24.0 \)[/tex]
5. Median (v): [tex]\( 13 \)[/tex]
6. Median weight: [tex]\( 50 \)[/tex] kg
7. Median age: [tex]\( 34 \)[/tex]
8. Position of median marks: [tex]\( \boxed{15} \)[/tex]
