The document discusses descriptive statistics and methods for presenting statistical data. Descriptive statistics involve organizing, summarizing, describing and interpreting data from an experiment or study. Data can be presented through tables and graphs. Tables present data in an organized, simple and easily interpreted manner, providing maximum information using minimum space. They must follow technical norms for construction. Statistical series summarize a set of observations according to time, space and variable studied, and can be simple or mixed.

1. ❈❛♣ít✉❧♦ ✷
❊st❛tíst✐❝❛ ❉❡s❝r✐t✐✈❛
❆ ❊st❛tíst✐❝❛ ❉❡s❝r✐t✐✈❛ é ❛ ❢❛s❡ ♥❛ q✉❛❧ ♦s ❞❛❞♦s ❞❡ ✉♠ ❡①♣❡r✐♠❡♥t♦ ♦✉ ♣❡sq✉✐s❛✱ sã♦
♦r❣❛♥✐③❛❞♦s✱ r❡s✉♠✐❞♦s✱ ❞❡s❝r✐t♦s✱ ❛♣r❡s❡♥t❛❞♦s ❡ ✐♥t❡r♣r❡t❛❞♦s✳ ❊st❛ ❢❛s❡ é ❞❡ ❣r❛♥❞❡
✐♠♣♦rtâ♥❝✐❛ ♣❛r❛ ✉♠❛ ♣❡sq✉✐s❛✱ ♣♦✐s ♥❡❧❛✱ ♣♦❞❡♠♦s ♣❡r❝❡❜❡r ❛s t❡♥❞ê♥❝✐❛s ❞♦ ♥♦ss♦ ❝♦♥❥✉♥t♦
❞❡ ❞❛❞♦s✳ ❆♣ós ❛ ❝♦❧❡t❛ ❞♦s ❞❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s✱ ❞❡✈❡♠♦s ♦r❣❛♥✐③á✲❧♦s ❡ ❛♣r❡s❡♥tá✲❧♦s❀ ❡st❛
❛♣r❡s❡♥t❛çã♦✱ ♣♦❞❡ s❡r ❢❡✐t❛ ❛tr❛✈és ❞❡ t❛❜❡❧❛s ❡ ❣rá✜❝♦s✳
✷✳✶ ❘❡♣r❡s❡♥t❛çã♦ ❚❛❜✉❧❛r
✷✳✶✳✶ ❚❛❜❡❧❛s
❆ ✜♥❛❧✐❞❛❞❡ ❞❛s t❛❜❡❧❛s é ❛♣r❡s❡♥t❛r ♦s ❞❛❞♦s ❞❡ ♠♦❞♦ ♦r❞❡♥❛❞♦✱ s✐♠♣❧❡s ❡ ❞❡ ❢á❝✐❧ ✐♥t❡r♣r❡t❛çã♦✱
❢♦r♥❡❝❡♥❞♦ ♦ ♠á①✐♠♦ ❞❡ ✐♥❢♦r♠❛çã♦ ♥✉♠ ♠í♥✐♠♦ ❞❡ ❡s♣❛ç♦✳
❆ ❝♦♥str✉çã♦ ❞❡ ✉♠❛ t❛❜❡❧❛✱ ❡♥tr❡t❛♥t♦✱ ❞❡✈❡ ♦❜❡❞❡❝❡r ❛ ✉♠❛ sér✐❡ ❞❡ ♥♦r♠❛s té❝♥✐❝❛s✳ ❊st❛s
♥♦r♠❛s ♣♦❞❡♠ s❡r ❡♥❝♦♥tr❛❞❛s ♥❛ ♣✉❜❧✐❝❛çã♦ ❞♦ ■❇●❊ ✐♥t✐t✉❧❛❞❛ ✏◆♦r♠❛s ❞❡ ❆♣r❡s❡♥t❛çã♦
❚❛❜✉❧❛r✧✳
❊❧❡♠❡♥t♦s ❞❛ ❚❛❜❡❧❛
✶✶

2. • ❚ít✉❧♦✿ é ❛ ✐♥❞✐❝❛çã♦ q✉❡ ♣r❡❝❡❞❡ ❛ t❛❜❡❧❛ ❝♦♥t❡♥❞♦ ❛ ❞❡s✐❣♥❛çã♦ ❞♦ ❢❛t♦ ♦❜s❡r✈❛❞♦✱ ♦
❧♦❝❛❧ ❡ ❛ é♣♦❝❛ ❡♠ q✉❡ ❢♦✐ ❡st✉❞❛❞♦✳
• ❈♦r♣♦✿ é ♦ ❝♦♥❥✉♥t♦ ❞❡ ❧✐❤❛s ❡ ❝♦❧✉♥❛s ♦♥❞❡ ❡stã♦ ✐♥s❡r✐❞♦s ♦s ❞❛❞♦s✳
• ❈❛❜❡ç❛❧❤♦✿ é ❛ ♣❛rt❡ s✉♣❡r✐♦r ❞❛ t❛❜❡❧❛ q✉❡ ✐♥❞✐❝❛ ♦ ❝♦♥t❡ú❞♦ ❞❛s ❝♦❧✉♥❛s✳
• ❈♦❧✉♥❛ ✐♥❞✐❝❛❞♦r❛✿ é ❛ ♣❛rt❡ ❞❛ t❛❜❡❧❛ q✉❡ ✐♥❞✐❝❛ ♦ ❝♦♥t❡ú❞♦ ❞❛s ❧✐♥❤❛s✳
❖s ❡❧❡♠❡♥t♦s ❝♦♠♣❧❡♠❡♥t❛r❡s sã♦✿
• ❋♦♥t❡✿ ❡♥t✐❞❛❞❡ q✉❡ ❢♦r♥❡❝❡ ♦s ❞❛❞♦s ♦✉ ❡❧❛❜♦r❛ ❛ t❛❜❡❧❛✳
• ◆♦t❛s✿ ✐♥❢♦r♠❛çõ❡s ❞❡ ♥❛t✉r❡③❛ ❣❡r❛❧✱ ❞❡st✐♥❛❞❛s ❛ ❡s❝❧❛r❡❝❡r ♦ ❝♦♥t❡ú❞♦ ❞❛s t❛❜❡❧❛s✳
• ❝❤❛♠❛❞❛s✿ ✐♥❢♦r♠❛çõ❡s ❡s♣❡❝í✜❝❛s ❞❡st✐♥❛❞❛s ❛ ❡s❝❧❛r❡❝❡r ♦✉ ❝♦♥❝❡✐t✉❛r ❞❛❞♦s ♥✉♠❛ ♣❛rt❡
❞❛ t❛❜❡❧❛✳
❖s ❡❧❡♠❡♥t♦s ❝♦♠♣❧❡♠❡♥t❛r❡s ❞❡✈❡♠ s✐t✉❛r✲s❡ ♥♦ r♦❞❛♣é ❞❛ t❛❜❡❧❛✱ ♥❛ ♠❡s♠❛ ♦r❞❡♠ ❡♠
q✉❡ ❢♦r❛♠ ❞❡s❝r✐t♦s✳
✷✳✶✳✷ ❙ér✐❡s ❊st❛tíst✐❝❛s
❆s sér✐❡s ❡st❛tíst✐❝❛s r❡s✉♠❡♠ ✉♠ ❝♦♥❥✉♥t♦ ♦r❞❡♥❛❞♦ ❞❡ ♦❜s❡r✈❛çõ❡s ❛tr❛✈és ❞❡ três ❢❛t♦r❡s
❢✉♥❞❛♠❡♥t❛✐s✿
• t❡♠♣♦✿ r❡❢❡r❡✲s❡ ❛ ❞❛t❛ ♦✉ ❛ é♣♦❝❛ ❡♠ q✉❡ ♦ ❢❡♥ô♠❡♥♦ ❢♦✐ ✐♥✈❡st✐❣❛❞♦❀
• ❡s♣❛ç♦✿ r❡❢❡r❡✲s❡ ❛♦ ❧♦❝❛❧ ♦✉ r❡❣✐ã♦ ♦♥❞❡ ♦ ❢❛t♦ ♦❝♦rr❡✉❀
• ❡s♣é❝✐❡✿ r❡❢❡r❡✲s❡ ❛♦ ❢❛t♦ ♦✉ ❢❡♥ô♠❡♥♦ q✉❡ ❡stá s❡♥❞♦ ✐♥✈❡st✐❣❛❞♦ ❡ ❝✉❥♦s ✈❛❧♦r❡s ♥✉♠ér✐❝♦s
❡stã♦ s❡♥❞♦ ❛♣r❡s❡♥t❛❞♦s✳
❆s sér✐❡s ❡st❛tíst✐❝❛s sã♦ ❝❧❛ss✐✜❝❛❞❛s ❞❡ ❛❝♦r❞♦ ❝♦♠ ♦ ❢❛t♦r q✉❡ ❡st✐✈❡r ✈❛r✐❛♥❞♦✱ ♣♦❞❡♥❞♦
s❡r s✐♠♣❧❡s ♦✉ ♠✐st❛s✳
✶✳ ❙ér✐❡s s✐♠♣❧❡s
• ❙ér✐❡ ❈r♦♥♦❧ó❣✐❝❛ ✭t❡♠♣♦r❛❧✱ ❤✐stór✐❝❛ ♦✉ ❡✈♦❧✉t✐✈❛✮✿ ♦♥❞❡ ✈❛r✐❛ ♦ t❡♠♣♦
♣❡r♠❛♥❡❝❡♥❞♦ ✜①♦s ♦ ❡s♣❛ç♦ ❡ ❛ ❡s♣é❝✐❡ ❞♦ ❢❡♥ô♠❡♥♦ ❡st✉❞❛❞♦✳
✶✷

3. ❚❛❜❡❧❛ ✷✳✶✿ Pr♦❞✉çã♦ ❞❡ P❡tró❧❡♦ ❇r✉t♦ ♥♦ ❇r❛s✐❧ ❞❡ ✶✾✼✻ ❛ ✶✾✽✵
❆♥♦s Pr♦❞✉çã♦
✶✾✼✻ ✾✳✼✵✷
✶✾✼✼ ✾✳✸✸✷
✶✾✼✽ ✾✳✸✵✹
✶✾✼✾ ✾✳✻✵✽
✶✾✽✵ ✶✵✳✺✻✷
✶
❋♦♥t❡✿ ❈♦♥❥✉♥t✉r❛ ❊❝♦♥ô♠✐❝❛ ✭❋❡✈ ✶✾✽✸✮
• ❙ér✐❡ ●❡♦❣rá✜❝❛ ✭❊s♣❛❝✐❛❧✱ ♦✉ ❚❡rr✐t♦r✐❛❧✱ ♦✉ ❞❡ ▲♦❝❛❧✐③❛çã♦✮✿ ♦♥❞❡ ✈❛r✐❛ ♦ ❡s♣❛ç♦
♣❡r♠❛♥❡❝❡♥❞♦ ✜①♦s ♦ t❡♠♣♦ ❡ ❛ ❡s♣é❝✐❡ ❞♦ ❢❡♥ô♠❡♥♦ ❡st✉❞❛❞♦✳
❚❛❜❡❧❛ ✷✳✷✿ ◆❡❝❡ss✐❞❛❞❡s ♠é❞✐❛s ❞❡ ❡♥❡r❣✐❛ ❡♠ ❛❧❣✉♥s ♣❛ís❡s✱ ❡♠ ✶✾✼✸✳
P❛✐s ❦❝❛❧✴♣❡r ❝❛♣✐t❛✴❞✐❛
❇r❛s✐❧ ✷✳✶✼✹
❊st❛❞♦s ❯♥✐❞♦s ✷✳✸✾✼
❊t✐ó♣✐❛ ✷✳✶✷✵
❏❛♣ã♦ ✶✳✶✷✺
▼é①✐❝♦ ✷✳✶✶✹
✷
❋♦♥t❡✿ ◆❡❝❡ss✐❞❛❞❡s ❍✉♠❛♥❛s ❞❡ ❊♥❡r❣✐❛ ✲ ■❇●❊
• ❙ér✐❡ ❡s♣❡❝✐✜❝❛t✐✈❛ ✭q✉❛❧✐t❛t✐✈❛ ♦✉ ❝❛t❡❣ór✐❝❛✿ ♦♥❞❡ ✈❛r✐❛ ❛ ❡s♣é❝✐❡ ♣❡r♠❛♥❡❝❡♥❞♦
✜①♦s ♦ t❡♠♣♦ ❡ ♦ ❡s♣❛ç♦ ❞♦ ❢❡♥ô♠❡♥♦ ❡st✉❞❛❞♦✳
❚❛❜❡❧❛ ✷✳✸✿ P♦♣✉❧❛çã♦ ❯r❜❛♥❛ ❡ ❘✉r❛❧ ❞♦ ❇r❛s✐❧ ❡♠ ✶✾✽✵ ✭① ✶✵✵✵✮✳
▲♦❝❛❧✐③❛çã♦ P♦♣✉❧❛çã♦
❯r❜❛♥❛ ✽✵✳✹✵✽
❘✉r❛❧ ✸✽✳✺✻✻
❚♦t❛❧ ✶✶✽✳✾✼✹
✸
❋♦♥t❡✿ ❆♥✉ár✐♦ ❊st❛tíst✐❝♦ ✭✶✾✽✹✮
✶✸

4. ✷✳ ❙ér✐❡s ♠✐st❛s✿ sã♦ ❛q✉❡❧❛s ❡♠ q✉❡ ♠❛✐s ❞❡ ✉♠ ❢❛t♦r ✈❛r✐❛ ♦✉ ✉♠ ❢❛t♦r ✈❛r✐❛ ♠❛✐s ❞❡ ✉♠❛
✈❡③✳
• ❙ér✐❡ ❤✐stór✐❝❛ ❣❡♦❣rá✜❝❛ ✭♦✉ ❣❡♦❣rá✜❝❛ ❤✐stór✐❝❛✮
❋✐❣✉r❛ ✷✳✶✿ ❚❛①❛ ❞❡ ❛t✐✈✐❞❛❞❡ ❢❡♠✐♥✐♥❛ ✉r❜❛♥❛✱ ❡♠ ♣❡r❝❡♥t✉❛❧✱ ❡♠ três r❡❣✐õ❡s ❞♦ ❇r❛s✐❧✱ ✶✾✽✶✱✾✵
• ❙ér✐❡ ❡s♣❡❝✐✜❝❛t✐✈❛ ❣❡♦❣rá✜❝❛ ✭♦✉ ❣❡♦❣rá✜❝❛ ❡s♣❡❝✐✜❝❛t✐✈❛✮
❋✐❣✉r❛ ✷✳✷✿ ❈♦♥s✉♠♦ ♣❡r ❝❛♣✐t❛ ❛♥✉❛❧ ❞❡ ❛❧❣✉♥s t✐♣♦s ❞❡ ❛❧✐♠❡♥t♦s✱ ❡♠ ❛❧❣✉♠❛s r❡❣✐õ❡s
♠❡tr♦♣♦❧✐t❛♥❛s ❞♦ ❇r❛s✐❧✱ ♥♦ ❛♥♦ ❞❡ ✶✾✽✽
• ❙ér✐❡ ❡s♣❡❝✐✜❝❛t✐✈❛ ❤✐stór✐❝❛ ✭♦✉ ❤✐stór✐❝❛ ❡s♣❡❝✐✜❝❛t✐✈❛✮
❋✐❣✉r❛ ✷✳✸✿ ❚❛①❛ ❞❡ ♠♦rt❛❧✐❞❛❞❡ ✭❡♠ ♣❡r❝❡♥t✉❛❧✮ ❞❡ ♠❡♥♦r❡s ❞❡ ✉♠ ❛♥♦ ♥♦ ❇r❛s✐❧✱ s❡❣✉♥❞♦ ❛s três
♣r✐♥❝✐♣❛✐s ❝❛✉s❛s✱ ♥♦ ♣❡rí♦❞♦ ❞❡ ✶✾✽✹ ❛ ✶✾✽✼
✶✹

5. • ❙ér✐❡ ❡s♣❡❝✐✜❝❛t✐✈❛ ❤✐stór✐❝❛ ❣❡♦❣rá✜❝❛
❋✐❣✉r❛ ✷✳✹✿ ◆ú♠❡r♦ ❞❡ ✈ít✐♠❛s ❡♠ ❛❝✐❞❡♥t❡s✱ s❡❣✉♥❞♦ ❛s ❣r❛♥❞❡s r❡❣✐õ❡s ❞♦ ❇r❛s✐❧✱ ♥♦s ❛♥♦s ❞❡
✶✾✾✶ ❡ ✶✾✾✷
✸✳ ❙ér✐❡ ❉✐str✐❜✉✐çã♦ ❞❡ ❢r❡q✉ê♥❝✐❛s✿ ♦❝♦rr❡ q✉❛♥❞♦ ♥❡♥❤✉♠ ❞♦s ❢❛t♦r❡s ✈❛r✐❛✳ ◆❡st❛ s❡r✐❡ ♦s
❞❛❞♦s sã♦ ❛❣r✉♣❛❞♦s ❡♠ ❝❧❛ss❡s s❡❣✉♥❞♦ s✉❛s r❡s♣❡❝✐t✈❛s ❢r❡q✉ê♥❝✐❛s✳ ❙❡❣✉♥❞♦ ❛ ♥❛t✉r❡③❛
❞♦s ❞❛❞♦s ❛s ❞✐str✐❜✉✐çõ❡s ❞❡ ❢r❡q✉ê♥❝✐❛s ♣♦❞❡♠ s❡r ❞❡ ❞♦✐s t✐♣♦s✿
• P❛r❛ ❞❛❞♦s ❞❡ ❡♥✉♠❡r❛çã♦
• P❛r❛ ❞❛❞♦s ❞❡ ♠❡♥s✉r❛çã♦
✶✺

6. ✷✳✷ ❉✐str✐❜✉✐çã♦ ❞❡ ❋r❡q✉ê♥❝✐❛
❯♠❛ ❞❛s ❢♦r♠❛s ❞❡ ♦r❣❛♥✐③❛r ❡ r❡s✉♠✐r ❛ ✐♥❢♦r♠❛çã♦ ❝♦♥t✐❞❛ ❡♠ ❞❛❞♦s ♦❜s❡r✈❛❞♦s é ♣♦r ♠❡✐♦
❞❡ t❛❜❡❧❛ ❞❡ ❢r❡qüê♥❝✐❛s ❡ ❣rá✜❝♦s✳
✷✳✷✳✶ ❚✐♣♦s ❞❡ ❢r❡qüê♥❝✐❛s
• ❋r❡qüê♥❝✐❛ s✐♠♣❧❡s ♦✉ ❛❜s♦❧✉t❛ ✭❋✮✿ ❙ã♦ ♦s ✈❛❧♦r❡s q✉❡ r❡❛❧♠❡♥t❡ r❡♣r❡s❡♥t❛♠ ♦ ♥ú♠❡r♦
❞❡ ❞❛❞♦s ❞❡ ❝❛❞❛ ❝❧❛ss❡✳
• ❋r❡qüê♥❝✐❛ r❡❧❛t✐✈❛ ✭❢r✮✿ ❙ã♦ ♦s ✈❛❧♦r❡s ❞❛s r❛③õ❡s ❡♥tr❡ ❛s ❢r❡qüê♥❝✐❛s s✐♠♣❧❡s ❡ ❛
❢r❡qüê♥❝✐❛ t♦t❛❧✳
• ❋r❡qüê♥❝✐❛ ❛❝✉♠✉❧❛❞❛ ✭❋❛✮✿ ➱ ♦ t♦t❛❧ ❞❛s ❢r❡qüê♥❝✐❛s ❞❡ t♦❞♦s ♦s ✈❛❧♦r❡s ✐♥❢❡r✐♦r❡s ❛♦
❧✐♠✐t❡ s✉♣❡r✐♦r ❞♦ ✐♥t❡r✈❛❧♦ ❞❡ ✉♠❛ ❞❛❞❛ ❝❧❛ss❡✳
• ❋r❡qüê♥❝✐❛ ❛❝✉♠✉❧❛❞❛ r❡❧❛t✐✈❛ ✭❋r✮✿ ➱ ♦ t♦t❛❧ ❞❛s ❢r❡qüê♥❝✐❛s r❡❧❛t✐✈❛s ❞❡ t♦❞♦s ♦s ✈❛❧♦r❡s
✐♥❢❡r✐♦r❡s ❛♦ ❧✐♠✐t❡ s✉♣❡r✐♦r ❞♦ ✐♥t❡r✈❛❧♦ ❞❡ ✉♠❛ ❞❛❞❛ ❝❧❛ss❡✳
✷✳✷✳✷ ❉✐str✐❜✉✐çã♦ ❞❡ ❋r❡qüê♥❝✐❛ ♣❛r❛ ❱❛r✐á✈❡✐s ◗✉❛♥t✐t❛t✐✈❛s ❈♦♥tí♥✉❛s
❖s ♣r✐♥❝✐♣❛✐s ❡stá❣✐♦s ♥❛ ❝♦♥str✉çã♦ ❞❡ ✉♠❛ ❞✐str✐❜✉✐çã♦ ❞❡ ❢r❡qüê♥❝✐❛ ♣❛r❛ ❞❛❞♦s ❝♦♥tí♥✉♦s
sã♦✿
• ❖r❣❛♥✐③❛r ♦s ❞❛❞♦s ❜r✉t♦s ❡♠ ✉♠ r♦❧ ❞❡ ♦r❞❡♠ ❝r❡s❝❡♥t❡ ♦✉ ❞❡❝r❡s❝❡♥t❡✳
✶✻