Math Homework

# What I have are buckets of response times (10ms, 25ms, 50ms,

etc) and for each request...
what I have are buckets of response times (10ms, 25ms, 50ms, etc) and for each request, it will increment the bucket counter by 1 that it falls in. For example, if a request took 30ms, the 50ms bucket will increase by 1.
Based off of this, is there a way I can calculate the response time median, 95th percentile, etc? (I'm aware some accuracy will be lost because of the bucketing)
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Customer reply replied 4 months ago
It has to be a single equation using only addition, subtraction, multiplication and/or division. Sample data:
response time: counts
10: 1780
25: 2010
50: 390
100: 390
150: 260
250: 300
500:(###) ###-#### 27
10000: 19
Customer reply replied 4 months ago
the 95th percentile for the above data should be around ~229 I think. But I need a single equation to get to this answer.
10/26/2017
Ryan, Engineer
Category: Math Homework
Satisfied Customers: 9,137
Experience: B.S. in Civil Engineering
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Hi,

Thank you for using the site. I'll be happy to help you with this.

The trick to determining the desired percentile value is that you must first determine which class of the frequency distribution your desired percentile falls in. So, for example, if you wanted the 90th percentile of a distribution that has a total of 200 responses, you need to determine which class contains the (0.90)(200) = 180th entry. This class is referred to as the "critical class" If you can do that, then the following formula will give you an approximation of the desired percentile.

n th percentile = L + [(P - c)(U - L) / f ]

where:

L is the lower limit of the critical class,

P is the desired index number of the value in the data set, (i.e. the 180th entry)

c is the cumulative frequency of all classes that come before the critical class,

U is the upper limit of the critical class, and

f is the frequency of the critical class.

For example, for the frequency distribution that you included above, the 95th percentile would correspond to the 5069.2th entry (0.95 * 5336 = 5069.2). The critical class is the 150-250 class. The values of the variables are then:

L = 150

P = 5069.2

c = 4830

f = 300

U = 250

The value of the 95th percentile is then approximately:

95th percentile = L + [ (P - c)(U - L) / f ]

= 150 + [ (5069.2 - 4830)(250 - 150) / 300

= 229.73

Thanks,

Ryan

Customer reply replied 4 months ago
Howdy Ryan,Unfortunately the application I'm using doesn't allow me to set if/else conditions so I can't do anything like "if P is 5069.2, then L is 150 and U is 250". Would it be possible to do it without any conditionals?Cheers,
Kelvin
That's the sticky part of this. To use that formula you need to know what class contains the desired percentile, and there isn't any way of just calculating it because it depends on the particular distribution.
Ryan, Engineer
Category: Math Homework
Satisfied Customers: 9,137
Experience: B.S. in Civil Engineering
Verified
Customer reply replied 4 months ago
That's a shame... Thanks a lot for your help!

You're quite welcome.

Ryan, Engineer
Category: Math Homework
Satisfied Customers: 9,137
9,137 Satisfied Customers
Experience: B.S. in Civil Engineering

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