# Problems from Absolute, relative, cumulative frequency and statistical tables

In a survey to $$20$$ inhabitants of Barcelona on how many times a week they buy in small shops in the city, the obtained answers are: $$2,0,3,1,4,5,1,1,2,3,0,0,1,3,2,5,4,3,3,2$$\$

Construct a frequency table and calculate what percentage of the population make purchases $$3$$ times or less per week in small shops.

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### Development:

 Purchases in small shops Absolute frequency $$f_i$$ Relative frequency $$n_i$$ Cumulative frequency $$F_i$$ Cumulative relative frequency $$N_i$$ $$0$$ $$3$$ $$\dfrac{3}{20}$$ $$3$$ $$\dfrac{3}{20}$$ $$1$$ $$4$$ $$\dfrac{4}{20}$$ $$3+4=7$$ $$\dfrac{7}{20}$$ $$2$$ $$4$$ $$\dfrac{4}{20}$$ $$3+4+4=11$$ $$\dfrac{11}{20}$$ $$3$$ $$5$$ $$\dfrac{5}{20}$$ $$11+5=16$$ $$\dfrac{16}{20}=0,8=80\%$$ $$4$$ $$2$$ $$\dfrac{2}{20}$$ $$16+2=18$$ $$\displaystyle\frac{18}{20}$$ $$5$$ $$2$$ $$\dfrac{2}{20}$$ $$18+2=20$$ $$\dfrac{20}{20}=1$$ $$\sum$$ $$20$$ $$1$$

### Solution:

 Purchases in small shops Absolute frequency $$f_i$$ Realtive frequency $$n_i$$ Cumulative frequency $$F_i$$ Cumulative relative frequency $$N_i$$ $$0$$ $$3$$ $$\dfrac{3}{20}$$ $$3$$ $$\dfrac{3}{20}$$ $$1$$ $$4$$ $$\dfrac{4}{20}$$ $$3+4=7$$ $$\dfrac{7}{20}$$ $$2$$ $$4$$ $$\dfrac{4}{20}$$ $$3+4+4=11$$ $$\dfrac{11}{20}$$ $$3$$ $$5$$ $$\dfrac{5}{20}$$ $$11+5=16$$ $$\dfrac{16}{20}=0,8=80\%$$ $$4$$ $$2$$ $$\dfrac{2}{20}$$ $$16+2=18$$ $$\displaystyle\frac{18}{20}$$ $$5$$ $$2$$ $$\dfrac{2}{20}$$ $$18+2=20$$ $$\dfrac{20}{20}=1$$ $$\sum$$ $$20$$ $$1$$

$$80\%$$ of the survey participants make purchases $$3$$ times or less per week in small shops.

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