public class Medical_Equipment_ControllerCls {

    public decimal totalAmount {get;set;}
    public decimal temp = 0;
    set<id> getid = new set<id>();
    public Medical_Equipment_ControllerCls(ApexPages.StandardController controller)
    {
        Medical_Equipment__c med = new Medical_Equipment__c();
        for(Medical_Equipment__c medical : [select name, Amount__c,Equipment_for_Department__c from Medical_Equipment__c])
        {
            getid.add(medical.Equipment_for_Department__c);
        }
        List<Medical_Equipment__c> lstmedical = [select Amount__c, Equipment_for_Department__c from Medical_Equipment__c where id in : getid and amount__c != null];
        for(Medical_Equipment__c medicalequp : lstmedical)
           {
                temp = temp + medicalequp.Amount__c;
                totalAmount = temp;
           }

    }
}

Select SUM(TotalAmount__c) from Department__c

public class Medical_Equipment_ControllerCls {

    public decimal totalAmount {get;set;}
    public decimal temp = 0;
    set<id> getid = new set<id>();
    public Medical_Equipment_ControllerCls(ApexPages.StandardController controller)
    {
        Medical_Equipment__c med = new Medical_Equipment__c();

         //****** Notice the changes in following query*****
        List<Medical_Equipment__c> lstmedical = [select Amount__c, Equipment_for_Department__c from Medical_Equipment__c where Equipment_for_Department__c!=null and amount__c != null];

         for(Medical_Equipment__c medicalequp : lstmedical)
           {
                temp = temp + medicalequp.Amount__c;
                totalAmount = temp;
           }

    }
}