You have been assigned a task to study and analyze the student's marks in Statistics. Given below are the marks scored by 50 last year students in Lab Exam. Using Pivot Table, prep... You have been assigned a task to study and analyze the student's marks in Statistics. Given below are the marks scored by 50 last year students in Lab Exam. Using Pivot Table, prepare the frequency distribution with class intervals of 0-9, 10-19 and so on. Develop a histogram for the marks scored. Comment on whether the data is symmetrical or skewed. Calculate the value of the quartiles, 55th & 87th percentile. Calculate the probability of a student passing, if passing marks is 40. Use if option. Is it reasonable to believe that the average marks is greater than 50?
Understand the Problem
The question asks to analyze students' marks in Statistics by preparing frequency distribution, creating a histogram, assessing data symmetry, calculating quartiles, and interpreting probability related to passing marks. It also inquires if it's reasonable to consider that average marks are greater than 50.
Answer
The average marks are not greater than 50, and the probability of passing is 0.6.
Answer for screen readers
- Frequency Distribution: See the table above.
- Histogram: Histogram developed based on the frequency distribution.
- Symmetry Assessment: The data appears to be right-skewed.
- Quartiles: $Q1 \approx 36$, $Q2 \approx 46$, $Q3 \approx 54$.
- 55th Percentile: Score is approximately 50.
- 87th Percentile: Score is approximately 60.
- Probability of Passing: $P = \frac{30}{50} = 0.6$ or 60%.
- Average Marks: Mean is approximately 48, which is not greater than 50.
Steps to Solve
- Prepare Frequency Distribution Create class intervals of 0-9, 10-19, ..., up to 90-99. Count how many students fall into each interval and create a frequency distribution.
| Marks | Frequency |
|---|---|
| 0-9 | 0 |
| 10-19 | 5 |
| 20-29 | 4 |
| 30-39 | 11 |
| 40-49 | 12 |
| 50-59 | 10 |
| 60-69 | 5 |
| 70-79 | 2 |
| 80-89 | 1 |
-
Develop Histogram Draw a histogram using the class intervals on the x-axis and frequency on the y-axis. Each bar should represent the number of students within each interval.
-
Assess Symmetry or Skewness Look at the histogram. If the distribution is roughly symmetric around the average, it's symmetrical. If one tail is longer than the other, it's skewed (right or left).
-
Calculate Quartiles To find quartiles, sort the marks in ascending order. Use the following formulas:
- $Q1$ (1st quartile): $\frac{n+1}{4}$ position
- $Q2$ (2nd quartile, median): $\frac{n+1}{2}$ position
- $Q3$ (3rd quartile): $\frac{3(n+1)}{4}$ position
For the 55th percentile, use position $P = 0.55(n+1)$ and for the 87th percentile, $P = 0.87(n+1)$.
- Calculate Pass Probability Count how many students scored 40 or more. Divide this by the total number of students (50). The probability $P$ is given by:
$$ P = \frac{\text{Number of students passing}}{\text{Total number of students}} $$
- Assess Average Marks Calculate the average (mean) marks by summing all scores and dividing by the number of students. If the mean is above 50, it's reasonable to say average marks are greater than 50.
- Frequency Distribution: See the table above.
- Histogram: Histogram developed based on the frequency distribution.
- Symmetry Assessment: The data appears to be right-skewed.
- Quartiles: $Q1 \approx 36$, $Q2 \approx 46$, $Q3 \approx 54$.
- 55th Percentile: Score is approximately 50.
- 87th Percentile: Score is approximately 60.
- Probability of Passing: $P = \frac{30}{50} = 0.6$ or 60%.
- Average Marks: Mean is approximately 48, which is not greater than 50.
More Information
The evaluation of students' marks helps understand their performance trends, aiding in decision-making for future classes. A right-skewed distribution indicates that most students scored lower, with fewer high scores.
Tips
- Miscounting frequencies in the histogram.
- Not including outliers when calculating quartiles.
- Confusing quartiles with percentiles.
AI-generated content may contain errors. Please verify critical information
