The table below shows the continuous assement scores obtained by 30 selected ss1 students in economics.
scores 1-5 6-10 11-15 16-20 21-25 26-30
frequency 2 5 3 10 8 2
(a) determine the mean score of the students.
(b) calculate the modal score.
answer?
(a) To determine the mean score of the students, we need to calculate the midpoint of each score interval and multiply it by the corresponding frequency. Then we add up all these products and divide by the total frequency.
Midpoint of interval 1-5 = (1+5)/2 = 3
Midpoint of interval 6-10 = (6+10)/2 = 8
Midpoint of interval 11-15 = (11+15)/2 = 13
Midpoint of interval 16-20 = (16+20)/2 = 18
Midpoint of interval 21-25 = (21+25)/2 = 23
Midpoint of interval 26-30 = (26+30)/2 = 28
Mean score = (2x3 + 5x8 + 3x13 + 10x18 + 8x23 + 2x28) / 30
Mean score = 15.6
Therefore, the mean score of the students is 15.6.
(b) The modal score is the score that appears most frequently in the data. From the table, we see that the highest frequency is 10, which corresponds to the score interval 16-20. Therefore, the modal score is 16-20.
To determine the mean score of the students, we need to calculate the weighted average of the scores.
Step 1: Find the midpoints of each score interval. To do this, we add the lower and upper bound of each interval and divide by 2.
Midpoint of 1-5: (1+5)/2 = 3
Midpoint of 6-10: (6+10)/2 = 8
Midpoint of 11-15: (11+15)/2 = 13
Midpoint of 16-20: (16+20)/2 = 18
Midpoint of 21-25: (21+25)/2 = 23
Midpoint of 26-30: (26+30)/2 = 28
Step 2: Multiply each midpoint by its corresponding frequency and sum them up.
(3*2) + (8*5) + (13*3) + (18*10) + (23*8) + (28*2) = 6 + 40 + 39 + 180 + 184 + 56 = 505
Step 3: Calculate the total frequency by summing up all the frequencies.
2 + 5 + 3 + 10 + 8 + 2 = 30
Step 4: Divide the total sum by the total frequency.
The mean score = 505/30 ≈ 16.83
Therefore, the mean score of the students is approximately 16.83.
To calculate the modal score, we need to find the score(s) that occur(s) most frequently.
In this case, the highest frequency is 10, which occurs for the score interval 16-20.
Therefore, the modal score is any score within the range 16-20.
So, the modal score is 16-20.