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It's been a while since I dealt with statistics, I guess I need to brush upon my knowledge about it but as I was reading an article for my class I had a hard time understanding the author's main point intuitively. Below is an excerpt from the article's abstract. The part where I had problem with is the meaning of a firm at the 90th percentile of growth rate distribution. Does this mean a firm whose growth rate was is higher than 90 percent of all firms, or a firm that is in the top 10 percentile in terms of growth rate?

"In 1999, a firm at the 90th percentile of the employment growth rate distribution grew about 31 percent faster than the median firm. Moreover, the 90-50 differential was 16 percent larger than the 50-10 differential reflecting the positive skewness of the employment growth rate distribution. We show that the shape of the firm employment growth distribution changes substantially in the post-2000 period. By 2007, the 90-50 differential was only 4 percent larger than the 50-10 ,and it continued to exhibit a trend decline through 2011. The overall decline reflects a sharp drop in the 90th percentile of the growth rate distribution accounted for by the declining share of young firms and the declining propensity for young firms to be high-growth firms."

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    $\begingroup$ You're fortunate here in that this was actually quite carefully worded, and intellgible with a little knowledge as given in answer(s). It is alarmingly common that people are fuzzy in writing about the top decile, the bottom quintile, or whatever. $\endgroup$
    – Nick Cox
    Nov 9, 2022 at 10:54
  • $\begingroup$ "in the post-2000 period" should be just "after 2000". Does no-one edit prose any more? (Indeed, nothing to do with the question". $\endgroup$
    – Nick Cox
    Nov 9, 2022 at 18:32

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Being at the 90th percentile means that you are higher than 90%, and lower than 10% of the population. This describes a point in the distribution.

Being in the top 10 percentile would mean that you are at the 90th percentile or higher. This describes a range in the distribution.

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    $\begingroup$ This is it and I've taken the liberty of adding emphasis, which is naturally reversible. As a quibble, I think "interval" is a slightly better word than "range". $\endgroup$
    – Nick Cox
    Nov 9, 2022 at 10:51
  • $\begingroup$ Let's say the growth rate is 10%. What I understand is firms that have 10% growth rate is growing more than the 90% of all the firm. However, after 2000 there is a decline in the growth rate of young firms. Therefore, the difference between 90-50 and 50-10 diminishes. Is that really so? I understand the theoretical standpoint but can't seem to incorporate it into practice. $\endgroup$ Nov 9, 2022 at 11:19
  • $\begingroup$ That seems to be a fair summary of the abstract. $\endgroup$ Nov 9, 2022 at 12:25

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