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a) Find the medians of the following sets of data.
[tex]\[
\begin{array}{lllllll}
\text{(i)} & 18, & 16, & 27, & 20, & 25 \\
\text{(ii)} & 21, & 28, & 14, & 42, & 35 \\
\text{(iii)} & 15, & 30, & 35, & 25, & 20, & 45, & 40 \\
\text{(iv)} & 22, & 16, & 14, & 26, & 32, & 30 \\
\text{(v)} & 16, & 13, & 10, & 14, & 11, & 12, & 15 \\
\end{array}
\][/tex]

b) The weights of five high school students are given below. Find their median weight.
[tex]\[
50 \text{ kg}, \quad 54 \text{ kg}, \quad 45 \text{ kg}, \quad 63 \text{ kg}, \quad 48 \text{ kg}
\][/tex]

c) Find the median age of a group of 7 people whose ages in years are as follows.
[tex]\[
47, 61, \quad 13, 34, \quad 56, 22, 8
\][/tex]

d) What is the position of the median marks in the table given below?
[tex]\[
\begin{tabular}{|l|c|c|c|c|c|}
\hline
Marks & 18 & 27 & 32 & 40 & 46 \\
\hline
No. of students & 2 & 3 & 10 & 9 & 5 \\
\hline
\end{tabular}
\][/tex]



Answer :

GinnyAnswer
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]

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