Answered

6. For the following data, calculate the median.

\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
Marks & 20 & 30 & 40 & 50 & 60 & 70 \\
\hline
\begin{tabular}{c}
Number of \\
Students
\end{tabular} & 5 & 10 & 15 & 20 & 25 & 5 \\
\hline
\end{tabular}



Answer :

GinnyAnswer
To calculate the median for the given data, follow these steps:

### Data Interpretation
You have two sets of data:
1. Marks: [20, 30, 40, 50, 60, 70]
2. Number of Students for each corresponding mark: [5, 10, 15, 20, 25, 5]

### Step 1: Construct the List of All Marks
Create a list that includes each mark repeated according to the number of students that received it.

#### List Construction:
- 20 repeated 5 times: [20, 20, 20, 20, 20]
- 30 repeated 10 times: [30, 30, 30, 30, 30, 30, 30, 30, 30, 30]
- 40 repeated 15 times: [40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40]
- 50 repeated 20 times: [50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50]
- 60 repeated 25 times: [60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60]
- 70 repeated 5 times: [70, 70, 70, 70, 70]

Combine all these sublists into one single list:
[tex]\[ [20, 20, 20, 20, 20, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 70, 70, 70, 70, 70] \][/tex]

### Step 2: Order the Data
The data is already ordered in increasing order: [tex]\[ [20, 20, 20, 20, 20, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 70, 70, 70, 70, 70] ### Step 3: Calculate the Length and Determine the Median Count the total number of students: \[5 + 10 + 15 + 20 + 25 + 5 = 80 \][/tex]

Since the number of observations (80) is even, the median is the average of the 40th and 41st numbers in the ordered list.
- The 40th number is 50
- The 41st number is also 50

### Step 4: Calculate the Median
The median is calculated as follows:
[tex]\[ \text{Median} = \frac{\text{40th number} + \text{41st number}}{2} = \frac{50 + 50}{2} = 50.0 \][/tex]

### Final Answer:
The median of the given data is:
[tex]\[ \boxed{50.0} \][/tex]