Question

4. The following table shows the marks scored by 100 students in a Mathematics
test of 80 marks:
Marks
0 - 20,20 - 30,30 - 40 ,,40 - 50 50-60, 60 - 70,70 - 80
No. of students 7 ,10 ,20 ,20 ,20, 15, 8
a) Find the probability that a student obtained:
i. Less than 20 marks.
ii. 60 or more marks.
b) Draw an ogive for the given distribution using a graph sheet. Use the graph to
estimate the following:
i. Interquartile range.
i. If scoring less than 35 marks is considered failed, find the number
of students who failed in the Mathematics test.​

Answer 1

Answer:

a)

I) 7/100

ii)(15+8)/100=23/100

b) calculate the cumulative sum, then plot the Ogive.

After drawing the Ogive, look for the value of N/4 for Q1 and 3N/4 for Q3 on the X axis and see where the touch the less than Ogive and the corresponding value of the Y axis shall give the quartile value.

InterQuartile range=Q3-Q1

The median of the data or the Q2 is the intersection of the more than and less than Ogives.

Similarly, look for the value 35 on the X axis and check for its corresponding Y axis value on the less than Ogive. It will give you the number of students scoring below 35 marks i.e. the number of students who failed maths.