I am having trouble with finding the 1st and 3rd quartiles of a set of data. For example, let's say the data is:
4, 9, 11, 16, and 24<- these are cumulative frequencies. The median (or 2nd percentile)is 11, right? My teacher says it's 12. Then for 3rd quartile I got 20, but my teacher says 18. Can someone explain to me what I am doing wrong?
Thanks.
The median is always the 50th percentile or 2nd quartile.
You seem to give frequencies (Y-axis/ordinate values), but do not give the quality/quantity in which these frequencies occur (X-axis/abscissa).
These are frequencies of what? Height? Weight? Test scores?
The quartiles would be given in terms of the abscissa values.
I hope this helps. If not, repost with more complete data. Thanks for asking.
To find the quartiles of a set of data, you need to first arrange the data in ascending order. In this case, the data is already in cumulative frequency form, so it needs to be converted back to its original form:
4, 5 (9-4), 2 (11-9), 5 (16-11), 8 (24-16)
Now, to find the median (which is the 2nd quartile), you need to find the cumulative frequency just greater than or equal to halfway through the total sum of frequencies. In this case, the total sum of frequencies is 24.
Since the median is the 2nd quartile, it represents the 50th percentile. So, you need to find the cumulative frequency just greater than or equal to 50% of 24, which is 12.
Looking at the data, we see that the cumulative frequency at position 2 is 5. Therefore, the median (2nd quartile) is in the class interval represented by the corresponding position, which is 11.
So, in this case, you are correct, and the median is indeed 11, not 12.
Now, to find the 1st quartile (25th percentile), you need to find the cumulative frequency just greater than or equal to 25% of 24, which is 6.
Looking at the data, we see that the cumulative frequency at position 2 is still 5. However, the cumulative frequency at position 3 is 7. Therefore, the 1st quartile is in the class interval represented by the corresponding position, which is 16.
So, the 1st quartile in this case is 16, not 18.
Similarly, to find the 3rd quartile (75th percentile), you need to find the cumulative frequency just greater than or equal to 75% of 24, which is 18.
Looking at the data, we see that the cumulative frequency at position 4 is 13. However, the cumulative frequency at position 5 is 21. Therefore, the 3rd quartile is in the class interval represented by the corresponding position, which is 24.
So, the 3rd quartile in this case is 24, not 20.
It seems there may have been a misunderstanding with your teacher's interpretation. Make sure to clarify this with them using the explanation provided here.