# Absolute, relative, cumulative frequency and statistical tables

## Problems

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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