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.

See development and solution

### 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.