Is the median from a cumulative frequency graph accurate?

[adjacent]

Homework Statement

Height- 1-10| 10-20 |30-50 |50-60
Frequency 2 |5| 7| 9
Cumulative frequency-2 7 14 18
So this is a Group frequency table.
Is the median obtained from Cumulative frequency graph 100% accurate?Or is it just an assumption?

Homework Equations

The Attempt at a Solution

We don't know the exact height value.So we put the largest value in the class.
So if just consider the first column,
The height of the first person(Frequency 1) should be 5.But we don't know that.He may or may not be 5feet(or whatever) tall

 

[Ray Vickson]

Homework Statement

Height- 1-10| 10-20 |30-50 |50-60
Frequency 2 |5| 7| 9
Cumulative frequency-2 7 14 18
So this is a Group frequency table.
Is the median obtained from Cumulative frequency graph 100% accurate?Or is it just an assumption?

Homework Equations

The Attempt at a Solution

We don't know the exact height value.So we put the largest value in the class.
So if just consider the first column,
The height of the first person(Frequency 1) should be 5.But we don't know that.He may or may not be 5feet(or whatever) tall

According to your table there is nobody between 20-30 units (whatever those are). Is that really the case?

Anyway, if you categorize more finely, you will get a different median. For example, if you use class boundaries 1-2, 2-3, 3-4, ..., 59-60 the answer will almost surely be different. In the first case you median will be accurate to +-5, and in the second case accurate to +-0.5 .

 

[adjacent]

According to your table there is nobody between 20-30 units (whatever those are). Is that really the case?

I just made up a graph from no where.It's the reason

Anyway, if you categorize more finely, you will get a different median. For example, if you use class boundaries 1-2, 2-3, 3-4, ..., 59-60 the answer will almost surely be different. In the first case you median will be accurate to +-5, and in the second case accurate to +-0.5 .

So it is an approximation.