The cumulative frequency curve above shoes the distribution of the scores of 50 students in an examination. Find the 36th percentile scores

Answer Details

To find the 36th percentile score, we need to locate the corresponding point on the cumulative frequency curve. The 36th percentile score is the score below which 36% of the data falls. First, we need to find the total frequency, which is 50 in this case. Then we calculate 36% of the total frequency: 36/100 x 50 = 18 This means that we are looking for the score below which 18 students have scored. We can locate this point on the cumulative frequency curve by drawing a horizontal line from 18 on the y-axis to where it intersects the curve. Then we draw a vertical line down to the x-axis to read off the corresponding score. From the curve, we can see that the 36th percentile score lies between 30 and 40. To estimate the exact score, we can use linear interpolation. The distance between 30 and 40 is 10, and the distance between the cumulative frequency at 30 (which is 16) and the cumulative frequency at 40 (which is 22) is 6. The distance from 30 to the 36th percentile score is: 10 x (18 - 16)/6 = 1.67 So the 36th percentile score is approximately: 30 + 1.67 = 31.67 Therefore, the answer is 28%.