Yes

you do need a jacket based on the weather in West Chester, PA 19383, USA 1 second ago

Why? Because it's cold. simple as that.
39°F4°C & Clear

Wind is 9 mph15 km/h from the NW, gusting to 22 mph36 km/h
March 29
4am39°F4°C10 mph16 km/h NWClear
5am37°F3°C10 mph17 km/h NWClear
6am36°F2°C10 mph16 km/h NWClear
7am35°F1°C9 mph15 km/h NWClear
8am36°F2°C9 mph14 km/h NWClear
9am40°F4°C10 mph15 km/h NWClear
10am44°F7°C11 mph18 km/h NWClear
11am47°F8°C12 mph20 km/h NWClear
12pm49°F9°C13 mph21 km/h NWMostly Clear
1pm51°F10°C14 mph22 km/h NWMostly Clear
2pm52°F11°C14 mph23 km/h NWMostly Clear
3pm53°F12°C15 mph24 km/h NWPartly Cloudy
DateLowHighWindDayNight
March 2935°F1°C54°F12°C13 mph20 km/h from NWMostly ClearClear
March 3033°F1°C58°F15°C7 mph12 km/h from WMostly CloudyMostly Cloudy
March 3147°F9°C61°F16°C8 mph13 km/h from NWPartly CloudyRain
April 144°F7°C51°F11°C7 mph11 km/h from ERainRain
April 243°F6°C50°F10°C8 mph13 km/h from ERainRain
April 340°F4°C49°F9°C9 mph15 km/h from NRainDrizzle
April 436°F2°C48°F9°C17 mph27 km/h from NWWindyPartly Cloudy

Yes

Low of 33°F1°C, High of 58°F15°C
Wind: 7 mph12 km/h
Precipitation: None

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