Let's solve these questions step-by-step using the information provided.
### 52. The mode of the distribution
The mode is the value that appears most frequently in a data set.
Looking at the frequency distribution:
- Marks: [tex]\(0, 1, 2, 3, 4, 5\)[/tex]
- Frequency: [tex]\(4, 7, 12, 18, 11, 8\)[/tex]
The highest frequency is 18, which corresponds to a mark of 3. Therefore, the mode of the distribution is:
Answer: (a) 3
### 53. Find the median of the distribution
The median is the middle value of a data set when the values are arranged in ascending order. If the total number of observations (n) is odd, the median is the middle value. If n is even, the median is the average of the two middle values.
First, let's calculate the cumulative frequency:
- Frequency: [tex]\(4, 7, 12, 18, 11, 8\)[/tex]
- Cumulative Frequency: [tex]\(4, 11, 23, 41, 52, 60\)[/tex]
The total number of observations (n) is:
[tex]\[ n = 4 + 7 + 12 + 18 + 11 + 8 = 60 \][/tex]
Since [tex]\( n = 60 \)[/tex], which is even, the median position is calculated as:
[tex]\[ \text{Median Position} = \left(\frac{60}{2} + \frac{60}{2} + 1\right) / 2 = 30.5 \][/tex]
We find the first cumulative frequency that is greater than or equal to 30.5, which is 41. This corresponds to a mark of 3. Therefore, the median of the distribution is:
Answer: (c) 3
### 54. How many pupils scored at least 2 marks?
To find the number of pupils who scored at least 2 marks, sum the frequencies of marks 2 and above:
[tex]\[ \text{Frequency for marks at least 2} = 12 + 18 + 11 + 8 = 49 \][/tex]
Therefore, the number of students who scored at least 2 marks is:
Answer: 49
### Summary of Answers:
- 52. The mode of distribution is: (a) 3
- 53. The median of the distribution is: (c) 3
- 54. The number of pupils who scored at least 2 marks is: 49
