following marks out of 75 full marks. A group of students took an entrance exam for an Engineering college and scored

Marks

20

30

40

50

60

70

the

Frequency

5

18

32

45

20

3

(a) On which axes should the marks and frequencies be shown to draw a histogram?

(b) Create a histogram for the provided data.

(c) What is the mark secured by the most number of students?

(d) If the pass-mark is 35, how many students will not make it to the engineering college

The Birthing Centre recorded the height of mothers as follows:

Let's break down the problem and answer each part step by step:

### (a) On which axes should the marks and frequencies be shown to draw a histogram?
- **Marks** should be shown on the **x-axis**.
- **Frequencies** should be shown on the **y-axis**.

### (b) Create a histogram for the provided data.
To create a histogram, the marks will be plotted on the x-axis, and the frequency of students securing those marks will be plotted on the y-axis. Here is how the data should be represented:

| Marks | Frequency |
|-------|-----------|
| 20    | 5         |
| 30    | 18        |
| 40    | 32        |
| 50    | 45        |
| 60    | 20        |
| 70    | 3         |

I can generate a visual histogram for this data.

### (c) What is the mark secured by the most number of students?
To determine the mark secured by the most number of students, we need to find the mark corresponding to the highest frequency. 

- The highest frequency is **45**, which corresponds to the mark **50**.

Thus, **50 marks** were secured by the most number of students.

### (d) If the pass-mark is 35, how many students will not make it to the engineering college?
To find the number of students who won't pass, sum the frequencies of students scoring below 35 marks.

- Students scoring **20 marks**: 5
- Students scoring **30 marks**: 18

Total students not passing = 5 + 18 = **23 students**.

### (e) The Birthing Centre recorded the height of mothers as follows:
Since this part of the question seems incomplete, please provide the height data if you want assistance with that as well.

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Do you want a detailed histogram, or any clarification on the above points? Here are some related questions:

1. How do you interpret a histogram in statistics?
2. What is the difference between a histogram and a bar graph?
3. How would you calculate the mean of the given marks?
4. How can you determine the median mark from this data?
5. What would be the cumulative frequency distribution for this data?

**Tip:** In a histogram, the area of the bar represents the frequency, so it's crucial to use consistent intervals on the x-axis.

Learn how to draw a histogram using marks and frequencies from an entrance exam for an Engineering college. Includes step-by-step instructions and analysis of student performance based on the data provided. Suitable for high school students studying statistics.

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