The mean for the exam marks of 450 students is the average score achieved by all 450 students. It is calculated by adding up all the individual scores and dividing by the total number of students (450). This gives an overall measure of the central tendency of the data.
The standard deviation for the exam marks of 450 students is a measure of the spread or variability of the data. It is calculated by finding the difference between each individual score and the mean, squaring those differences, adding them up, dividing by the total number of students (450), and then taking the square root. This gives an overall measure of how much the scores deviate from the mean.
The normal distribution is a commonly used distribution in statistics and is often used to model real-world data, including exam marks. It is a bell-shaped curve that is symmetrical and has a defined mean and standard deviation. This makes it a useful tool for understanding the distribution of scores and identifying any potential outliers or trends in the data.
Yes, the mean and standard deviation can be used to make predictions about future exam marks. By understanding the distribution of scores and the variability within the data, we can estimate the likelihood of certain scores occurring in future exams. However, it is important to note that there are other factors that can also impact exam scores, so these predictions may not always be accurate.
The mean and standard deviation can be used to compare the performance of different groups of students by calculating these measures for each group and then comparing them. This can help identify any significant differences or similarities in the exam marks between the groups. However, it is important to consider any potential confounding factors that may impact the results, such as differences in study habits or prior knowledge.