mongo group and count with condition

What you need is the $cond operator of aggregation framework. One way to get what you want would be:

db.foo.aggregate([
    {
        $project: {
            item: 1,
            lessThan10: {  // Set to 1 if value < 10
                $cond: [ { $lt: ["$value", 10 ] }, 1, 0]
            },
            moreThan10: {  // Set to 1 if value > 10
                $cond: [ { $gt: [ "$value", 10 ] }, 1, 0]
            }
        }
    },
    {
        $group: {
            _id: "$item",
            countSmaller: { $sum: "$lessThan10" },
            countBigger: { $sum: "$moreThan10" }
        }
    }
])

Note: I have assumed value to numeric rather than String.

Output:

{
        "result" : [
                {
                        "_id" : "xyz1",
                        "countSmaller" : 1,
                        "countBigger" : 0
                },
                {
                        "_id" : "abc1",
                        "countSmaller" : 2,
                        "countBigger" : 2
                }
        ],
        "ok" : 1
}  

You need to use the $cond operator. Here 0 is value less than 10 and 1 value greater than 10. This doesn't exactly give you expected output. Perhaps someone will post better answer.

db.collection.aggregate(
    [
        {
            "$project": 
                {
                    "item": 1, 
                    "value": 
                        {
                            "$cond": [ { "$gt": [ "$value", 10 ] }, 1, 0 ] 
                        }
                 }
         }, 
         {
             "$group": 
                 {
                     "_id": { "item": "$item", "value": "$value" },                       
                     "count": { "$sum": 1 }
                 }
         }, 
         {
             "$group": 
                 { 
                     "_id": "$_id.item", 
                     "stat": { "$push": { "value": "$_id.value", "count": "$count" }}
                 }
          }
    ]
)

Output:

{
        "_id" : "abc1",
        "stat" : [
                {
                        "value" : 1,
                        "count" : 2
                },
                {
                        "value" : 0,
                        "count" : 2
                }
        ]
}
{ "_id" : "xyz1", "stat" : [ { "value" : 0, "count" : 1 } ] }

You will need to convert your value to integer or float