I've got a set of data split into age groups and the number of people in each age group. I want to test if the number of people in one of the age groups is statistically significantly larger than the mean. Is this possible and what test do I use? I've looked at using a t test but it makes no sense with a population size of one.

For example :

Age Range Frequency

>=15 and <=20 100

>20 and <=25 256

>25 and <=30 278

>30 and <=35 313

>35 and <=40 356

>40 and <=45 489

>45 and <=50 510

>50 and <=55 567

>55 and <=60 620

>60 and <=65 677

>65 and <=70 712

>70 and <=75 707

>75 and <=80 512

>80 and <=85 310

>85 and <=90 178

>90 and <=95 32

>95 and <=100 0

And I want to find out whether one of the frequencies is statistically significantly different to the mean? I've scoured online but I can't find any examples of this type of problem at all. Or, rather than a test of any sort, would I just work out the standard deviation and, assuming I want a 95% confidence level, work out 1.96 times the standard deviation and say that anything 1.96 standard deviations above or below the mean is statistically significantly different?

Thanks in advance

For example :

Age Range Frequency

>=15 and <=20 100

>20 and <=25 256

>25 and <=30 278

>30 and <=35 313

>35 and <=40 356

>40 and <=45 489

>45 and <=50 510

>50 and <=55 567

>55 and <=60 620

>60 and <=65 677

>65 and <=70 712

>70 and <=75 707

>75 and <=80 512

>80 and <=85 310

>85 and <=90 178

>90 and <=95 32

>95 and <=100 0

And I want to find out whether one of the frequencies is statistically significantly different to the mean? I've scoured online but I can't find any examples of this type of problem at all. Or, rather than a test of any sort, would I just work out the standard deviation and, assuming I want a 95% confidence level, work out 1.96 times the standard deviation and say that anything 1.96 standard deviations above or below the mean is statistically significantly different?

Thanks in advance

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