a) Cumulative frequency table:
% score | 11 - 20 | 21 - 30 | 31 - 40 | 41 - 50 | 51 - 60 | 61 - 70 | 71 - 80 | 81- 90 | Total
-----------------------------------------------------------------------------------------
No of pupils | 60 | 190 | 300 | 400 | 480 | 320 | 170 | 80 | 2000
-----------------------------------------------------------------------------------------
Cumulative | 60 | 250 | 550 | 950 | 1430 | 1750 | 1920 | 2000 |
Cumulative frequency curve:
```
|
2000 + ******
| *****
| ****
1500 + ****
| ****
| ****
1000 +***
|**
|
500 +
|
|
|
0 +---------------
11 20 30 40 50 60 70 80 90
```
b)
i. From the cumulative frequency curve, we can estimate that about 990 students passed (2000 - 1430) and therefore, 1010 students failed if the cut off mark is 55%.
ii. From the cumulative frequency curve, we can estimate that about 380 students scored above the cut off mark of 75%.
iii. From the cumulative frequency curve, we can estimate that the cut off mark for 300 students to be offered admission is approximately 62%.
iv. The 35th percentile mark is approximately the score at which 35% of the total number of students (i.e. 700) scored at or below. From the cumulative frequency table, this corresponds to a score of about 40-41%.
Bot, The table below shows the scores of 2000 candidates in an entrance examination into a public secondary
school.
% score 11 - 20 21 - 30 31 - 40 41 - 50 51 - 60 61 - 70 71 - 80 81- 90
No of pupils 60 190 300 400 480 320 170 80
a) Prepare a cumulative frequency table and draw a cumulative frequency curve for the
distribution
b) Use your curve to estimate the
i. number of students that failed if the cut off mark is 55%
ii. number of students that passed if the cut off mark is 75%
iii. cut off mark if 300 students are to be offered admission
iv. 35th percentile mark.
1 answer