Mean, Median, and Mode Calculation
- Mean Calculation:
To calculate the mean score, we need to multiply each score by its frequency, then sum up all the products and divide by the total number of scores.
Mean = (40*2 + 50*4 + 60*7 + 70*9 + 80*5 + 90*3) / (2 + 4 + 7 + 9 + 5 + 3)
Mean = (80 + 200 + 420 + 630 + 400 + 270) / 30
Mean = 2000 / 30
Mean = 66.67
- Median Calculation:
To calculate the median score, we arrange the scores in ascending order and find the middle value. Since we have 30 scores in total, the median will be the average of the 15th and 16th values when arranged in ascending order.
The 15th and 16th values fall in the 70-79 range. Therefore, the median score is 75.
- Mode Calculation:
The mode is the score that appears most frequently in the distribution. In this case, the score range with the highest frequency is 70-79 with a frequency of 9. Therefore, the mode score is in the range of 70-79.

Explanation:
- Mean: The mean score of the mathematics contest is calculated by summing up all the scores and dividing by the total number of scores. In this case, the mean score is 66.67, indicating the average performance of the participants.
- Median: The median score represents the middle value when all scores are arranged in ascending order. In this case, the median score is 75, showing the central tendency of the scores.
- Mode: The mode score is the most frequently occurring score in the distribution. In this case, the mode score falls in the 70-79 range, indicating the score range with the highest frequency among participants.