Doppler radar (HB100) Arduino code : Why do we use bit-shifting? - arduino

Question

I've been working on my doppler radar speed project for a while. I found this very helpful link and the code below:
// Based on the Adafruit Trinket Sound-Reactive LED Color Organ
// http://learn.adafruit.com/trinket-sound-reactive-led-color-organ/code
#define RADAR A5 // RADAR inut is attached to A7
#define MICRODELAY 100 // 100microseconds ~10000hz
#define MAXINDEX 1024 // 10 bits
#define TOPINDEX 1023 // 10 bits
byte collect[MAXINDEX];
int mean;
int minimum;
int maximum;
int hysteresis; // 1/16 of max-min
bool currentphase; // are value above mean + hysteresis;
int lastnull; // index for last null passing value
int prevnull; // index for previous null passing value
int deltaindex;
int deltadeltaindex;
int index;
bool phasechange = false;
void setup() {
// put your setup code here, to run once:
Serial.begin(115200);
while (!Serial) {}
index = 0;
mean = 0;
maximum = 255;
minimum = 0;
hysteresis = 0;
currentphase = false;
lastnull = 0;
prevnull = 0;
Serial.print("deltadeltaindex");
Serial.print("\t");
Serial.print("deltaindex");
Serial.print("\t");
Serial.println("delta");
}
void loop() {
int newVal = analogRead(RADAR); // Raw reading from amplified radar
mean -= (collect[index] >> 2);
mean += (newVal >> 2);
collect[index]= newVal;
minimum = newVal < minimum ? newVal : minimum + 1;
maximum = newVal > maximum ? newVal : maximum - 1;
hysteresis = abs(maximum - minimum) >> 5;
if(newVal > (mean + hysteresis))
{
if(false == currentphase)
{
currentphase = true;
phasechange = true;
}
}
else if(newVal < (mean - hysteresis))
{
if(currentphase)
{
currentphase = false;
phasechange = true;
}
}
if(phasechange)
{
prevnull = lastnull;
lastnull = index;
int delta = (prevnull > lastnull) ?
(lastnull - prevnull + MAXINDEX) :
(lastnull - prevnull);
deltadeltaindex = abs(deltaindex - delta);
deltaindex = delta;
Serial.print(deltadeltaindex);
Serial.print("\t");
Serial.print(deltaindex);
Serial.print("\t");
Serial.println(delta);
}
index = index == TOPINDEX ? 0 : index + 1;
phasechange = false;
//delayMicroseconds(10);
}
I tried it out on my Arduino with HB100(model with breakout board), and it works just fine.
However, what I really wanted to do was to understand the mechanism behind the code. I read some articles on hysteresis and bit-shifting, but I simply cannot understand why the programmer here used bit-shifting.
What would mean -= (collect[index] >> 2); and mean += (newVal >> 2); do to the values exactly?
Help will be appreciated.