When calculating percentiles, ie the 33rd percentile, do you use the lower limit of the group that contains the 33rd
percentile? as in this case:
70-79 11 46 80.7
60-69 9 35 61.4
50-59 8 26 45.61
40-49 7 18 31.58
Would you use the number 49.5??
Thank you for using the Jiskha Homework Help Forum. If I understand your question the 1/3 (by the rule of math) would be the lower percentile. 2/3 would be higher. The demarcation is the 1/2.
It might be better if you interpolated within the interval to get the 33rd percentile more exactly.
For example, if 70 was the 30th percentile and 79 was the 40th, then 73 would be the 33rd percentile.
I hope this helps a little more. Thanks for asking.
When calculating percentiles, you use the lower limit of the group that contains the percentile you are interested in.
In the given example, the percentile you are looking for is the 33rd percentile. To determine which group contains the 33rd percentile, we need to calculate the cumulative frequency.
The cumulative frequency is the total frequency up to a particular group. To calculate the cumulative frequency, you add up the frequencies of all the groups before the group you are interested in.
For example, for the first group (70-79), the cumulative frequency is simply its own frequency, which is 11.
For the second group (60-69), the cumulative frequency is the sum of the frequency of the first and second groups, which is 11 + 9 = 20.
Similarly, for the third group (50-59), the cumulative frequency is the sum of the frequency of the first, second, and third groups, which is 11 + 9 + 8 = 28.
Once you have the cumulative frequencies, you can determine which group contains the 33rd percentile. In this case, the 33rd percentile falls within the second group (60-69) because its cumulative frequency is greater than or equal to 33.
To calculate the value for the 33rd percentile, you can use interpolation. Interpolation determines where within the range of the group the percentile falls.
In this example, the second group (60-69) has a cumulative frequency of 20, and the previous group (70-79) has a cumulative frequency of 11. To calculate the interpolated value for the 33rd percentile, you can use the following formula:
(interpolated value) = (lower limit of the group) + [(percentage distance within the group) * (width of the group)]
The percentage distance within the group can be calculated as (cumulative frequency - frequency of previous group) / frequency of current group.
In this case, (20 - 11) / 9 = 1
Using this formula, you would calculate the 33rd percentile as:
(interpolated value) = 60 + (1 * (69-60)) = 60 + (1 * 9) = 69
Therefore, when finding the 33rd percentile in this example, you would use the number 69.