In an examination two students scored $$ 40 \% $$, five students scored $$ 50 \% $$, four students scored $$ 55 \% $$, five students scored $$ 60 \% $$, three students scored $$ 65 \% $$, four students scored $$ 70 \% $$, and two students scored $$ 75 \% $$.

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UpStudy AI · Accepted Answer

Certainly! Let's analyze the examination scores of the students you've provided. We'll calculate several key statistical measures, including the **total number of students**, **mean (average) score**, **median**, **mode**, and **range**.

### Given Data:
- **40%**: 2 students
- **50%**: 5 students
- **55%**: 4 students
- **60%**: 5 students
- **65%**: 3 students
- **70%**: 4 students
- **75%**: 2 students

### 1. Total Number of Students

To find the total number of students, sum the number of students in each score category:

$$
\text{Total Students} = 2 + 5 + 4 + 5 + 3 + 4 + 2 = 25 \text{ students}
$$

### 2. Mean (Average) Score

The mean score is calculated by multiplying each score by the number of students who achieved it, summing these products, and then dividing by the total number of students.

$$
\text{Mean} = \frac{(40 \times 2) + (50 \times 5) + (55 \times 4) + (60 \times 5) + (65 \times 3) + (70 \times 4) + (75 \times 2)}{25}
$$

$$
\text{Mean} = \frac{80 + 250 + 220 + 300 + 195 + 280 + 150}{25} = \frac{1475}{25} = 59\%
$$

**Mean Score:** **59%**

### 3. Median Score

The median is the middle value when all scores are ordered from lowest to highest. Since there are 25 students (an odd number), the median is the 13th score in the ordered list.

**Ordered List with Cumulative Counts:**
1. 40% (1st student)
2. 40% (2nd student)  
3. 50% (3rd student)
4. 50% (4th student)
5. 50% (5th student)
6. 50% (6th student)
7. 50% (7th student)
8. 55% (8th student)
9. 55% (9th student)
10. 55% (10th student)
11. 55% (11th student)
12. 60% (12th student)
13. 60% (13th student) ← **Median**
14. 60% (14th student)
15. 60% (15th student)
16. 60% (16th student)
17. 65% (17th student)
18. 65% (18th student)
19. 65% (19th student)
20. 70% (20th student)
21. 70% (21st student)
22. 70% (22nd student)
23. 70% (23rd student)
24. 75% (24th student)
25. 75% (25th student)

**Median Score:** **60%**

### 4. Mode

The mode is the score that appears most frequently. From the data:

- **50%**: 5 students
- **60%**: 5 students

Both **50%** and **60%** are the most frequent scores, each occurring **5 times**.

**Mode:** **50% and 60%** (Bimodal)

### 5. Range

The range is the difference between the highest and lowest scores.

$$
\text{Range} = \text{Highest Score} - \text{Lowest Score} = 75\% - 40\% = 35\%
$$

**Range:** **35%**

### Summary

- **Total Students:** 25
- **Mean Score:** 59%
- **Median Score:** 60%
- **Mode:** 50% and 60%
- **Range:** 35%

If you need further analysis or visualization of this data (such as a frequency distribution table or graphical representations like histograms or bar charts), feel free to ask!
**Summary of Examination Scores:** - **Total Students:** 25 - **Mean Score:** 59% - **Median Score:** 60% - **Mode:** 50% and 60% - **Range:** 35%

In an examination two students scored \( 40 \% \), five students scored \( 50 \% \), four students scored \( 55 \% \), five students scored \( 60 \% \), three students scored \( 65 \% \), four students scored \( 70 \% \), and two students scored \( 75 \% \).

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