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I would like to know if I have interpreted the following statement correctly and would be grateful of any help at all.

"The unemployment rate for 16-24 year olds not in full-time education was 12.2%"

I read this as the proportion of economically active 16-24 year olds that are not in full-time education and unemployed is 12.2%.

To clarify I believe it says $$12.2\%=\frac{\text{economically active (full time education and unemployed)}}{\text {economically active (FTE unemployed + FTE employed)}}$$

Is this correct? I have looked online and have only seen the term unemployment rate in terms of the general population.

I am not an economist but a maths teacher and require the information to understand material for an upcoming context based exam. I have no trouble with percentages but need to make sure I have interpreted the economics correctly.

Thanks in advance for any clarifications.

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No, it's not correct. You are supposed to exclude people in FTE from labour force. Unemployment rate is a proportion of labour force which is unemployed. Labour force is defined as a sum of those employed and those looking for jobs (so it also excludes pensioners, parents on parental leave etc.). In your example the labour force should consist of only the people 16-24 years old.

I.e. $$12.2\% = \frac{\text{unemployed who are 16-24 years old}}{\text{labour force who are 16-24 years old (employed + unemployed)}}$$

Edit: I added that in this example labour force is restricted to specified age group.

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    $\begingroup$ To be precise, the labour force refers only to those in the 16-24 age group, not in FTE. The unemployed refers to the subgroup of them, which are not employed but looking for jobs. $\endgroup$ – luchonacho May 1 '17 at 13:24
  • $\begingroup$ To clarify: when you say unemployed in the numerator you are referring to those unemployed 16-24 year old son not in full time education and are economically active? Sorry for my ignorance I've never studied this before now. $\endgroup$ – Karl May 1 '17 at 13:26
  • $\begingroup$ Yes, this is true, thanks. I added an edit to clarify. $\endgroup$ – ElChorro May 1 '17 at 13:26
  • $\begingroup$ no reason to be sorry! Yes, if you are interested in any statistic for a particular group (in your case 16-24 y.o.) you should always exclude the people not in this group from the population. In my original answer I wanted to highlight that for the purpose of calculating unemployment, people in FTE are excluded. $\endgroup$ – ElChorro May 1 '17 at 13:31

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