total
number of students = 10+15+ 30+32+8+5 = 100

total
marks obtained = 15 * 10 + 25 * 15 + 35 * 30 + 45 * 32 + 55 * 8 + 65* 5 ] = 3780

*mean of the marks = 3780 / 100 = 37.80**
*

Ogive curve is for plotting the cumulative frequency distribution of students against the less than or more than or mid-points of the marks intervals.

We calculate the Median or 50% percentile or 25 percentile or some other. ** We do not find the mean of the values by using Ogive curve. It is median we can find**.

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Marks < 10 < 20 < 30 < 40 < 50 < 60 < 70

number of

Students 0 10 15 30 32 8 5

Cumulative 0 10 25 55 87 95 100

frequency

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From the cumulative frequency row, 50th student is in the interval 30-40. We say the median is 40 marks. If we take the midpoint of this interval, then we say that median is 35 marks.

*From the graph:*

Plotting these data values and drawing the graph , gives us the less than ogive curve. Then at 50% of students size, ie., at 100/2 = 50, draw a line from Y axis horizontally. It cuts the ogive curve. Then draw vertical line from there. Read the marks at that point. That is the median.

*For the data using less than ogive curve we get : median = 38. marks.*

If we had drawn the normal Ogive using the midpoints of the intervals, then median would be 33 marks.