Data Smoothing by Using Median Binning Technique

We have data for student’s income (in thousand rupiahs) while doing part time job along last

holiday like below:

a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t,

u, v, w, x, y, z, aa

a = 41 * 10 = 410               b = 41 * 15 = 615               c = 41 * 13 = 533

d = 41 * 12 = 492                e = 41 * 19 = 779              f = 41 * 16 = 656

g = 41 * 17 = 697               h = 41 * 18 = 738               i = 41 * 14 = 574

j = 41 * 23 = 943                k = 41 * 29 = 1189             l = 41 * 26 = 1066

m = 41 * 35 = 1435           n = 41 * 24 = 984               o = 41 * 25 = 1025

p = 41 * 31 = 1271             q = 41 * 32 = 1312             r = 41 * 28 = 1148

s = 41 * 13 = 533                t = 41 * 20 = 820                u = 41 * 34 = 1394

v = 41 * 27 = 1107             w = 41 * 33 = 1353            x = 41 * 50 = 2050

y = 41 * 43 = 1763             z = 41 * 11 = 451                aa = 41 * 37 = 1517

We can smooth the data by using Median Binning Technique below :

1). Sorting the data

410, 451, 492, 533, 533, 574, 615, 656, 697, 738, 779, 820, 943, 984, 1025, 1066, 1107, 1148, 1189, 1271, 1312, 1353, 1394, 1435, 1517, 1763, 2050

2). Partition into (equal-frequency) bins

Bin 1 :  410, 451, 492

Bin 2 :  533, 533, 574

Bin 3 :  615, 656, 697

Bin 4 :  738, 779, 820

Bin 5 :  943, 984, 1025

Bin 6 :  1066, 1107, 1148

Bin 7 :  1189, 1271, 1312

Bin 8 :  1353, 1394, 1435

Bin 9 :  1517, 1763, 2050

3). Smooting by bin medians

Bin 1 :  451, 451, 451

Bin 2 :  533, 533, 533

Bin 3 :  656, 656, 656

Bin 4 :  779, 779, 779

Bin 5 :  984, 984, 984

Bin 6 :  1107, 1107, 1107

Bin 7 :  1271, 1271, 1271

Bin 8 :  1394, 1394, 1394

Bin 9 :  1763, 1763, 1763

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