How can I save my float 'ave' on the EEPROM continuously? How can I save my output continuously to EEPROM? Or is this even possible? Please help me out.

void setup() {
  Serial.begin(9600);
}

void loop() {
  static unsigned long count = 0;
  static float sum = 0;
  float ave = 0;
  int volt = analogRead(A1);
  float voltage = map(volt, 0, 1023, 0, 2500) / 100.0;
  Serial.print("Voltage: ");
  Serial.println(voltage, 2);
  sum = sum + voltage;
  count++;
  ave = sum / count;
  Serial.print("Average: ");
  Serial.println(ave, 2);
  Serial.println("-----");
  delay(3000);
}
It's possible, but it's certainly not advised.

EEPROM has a limited number of writes before it's dead. By writing continuously to the EEPROM you will kill it in no time at all.