Discrepancy in Obtaining Quartile Count Using cut() and length() Functions in R

Question

Let us consider the following array

x<-c(0.385, 0.385, 0.311, 0.311, 0.585, 0.585, 0.352, 
0.352, 0.359, 0.359, 0.627, 0.627, 0.329, 0.329, 
0.296, 0.296, 0.504, 0.504, 0.456, 0.456, 0.281, 
0.281, 0.335, 0.335, 0.356, 0.356, 0.368, 0.368, 
0.326, 0.326, 0.487, 0.487, 0.323, 0.323, 0.710, 
0.710, 0.437, 0.437, 0.387, 0.387, 0.550, 0.550, 
0.363, 0.363, 0.342, 0.342, 0.344, 0.344, 0.516, 
0.516, 0.351, 0.351, 0.282, 0.282, 0.444, 0.444, 
0.356, 0.356, 0.437, 0.437, 0.369, 0.369, 0.282, 
0.282, 0.312, 0.312, 0.336, 0.336, 0.556, 0.556, 
0.464, 0.464, 0.274, 0.274, 0.352, 0.352, 0.362, 
0.362, 0.238, 0.238, 0.385, 0.385, 0.274, 0.274, 
0.411, 0.411, 0.300, 0.300, 0.355, 0.355, 0.381, 
0.381, 0.264, 0.264, 0.343, 0.343, 0.336, 0.336, 
0.279, 0.279, 0.493, 0.493, 0.290, 0.290, 0.578, 
0.578, 0.371, 0.371, 0.430, 0.430, 0.433, 0.433, 
0.341, 0.341, 0.335, 0.335, 0.414, 0.414, 0.372, 
0.372, 0.297, 0.297, 0.320, 0.320, 0.348, 0.348, 
0.299, 0.299, 0.368, 0.368, 0.569, 0.569, 0.284, 
0.284, 0.371, 0.371, 0.349, 0.349, 0.290, 0.290, 
0.540, 0.540, 0.664, 0.664, 0.540, 0.540, 0.587, 
0.587, 0.348, 0.348, 0.346, 0.346, 0.358, 0.358, 
0.423, 0.423, 0.520, 0.520, 0.392, 0.392, 0.355, 
0.355, 0.276, 0.276, 0.529, 0.529, 0.440, 0.440, 
0.351, 0.351, 0.453, 0.453, 0.418, 0.418, 0.439, 
0.439, 0.340, 0.340, 0.426, 0.426, 0.333, 0.333, 
0.421, 0.421, 0.420, 0.420, 0.373, 0.373, 0.378, 
0.378, 0.364, 0.364, 0.401, 0.401, 0.303, 0.303, 
0.634, 0.634, 0.285, 0.285, 0.344, 0.344, 0.602, 
0.602, 0.320, 0.320, 0.393, 0.393, 0.358, 0.358, 
0.360, 0.360, 0.548, 0.548, 0.321, 0.321, 0.318, 
0.318, 0.328, 0.328, 0.338, 0.338, 0.404, 0.404, 
0.420, 0.420, 0.373, 0.373, 0.245, 0.245, 0.487, 
0.487, 0.653, 0.653, 0.339, 0.339, 0.331, 0.331, 
0.593, 0.593, 0.398, 0.398, 0.273, 0.273, 0.452, 
0.452, 0.425, 0.425, 0.291, 0.291, 0.287, 0.287, 
0.430, 0.430, 0.357, 0.357, 0.289, 0.289, 0.626, 
0.626, 0.360, 0.360, 0.482, 0.482, 0.484, 0.484, 
0.307, 0.307, 0.344, 0.344, 0.325, 0.325, 0.421, 
0.421, 0.373, 0.373, 0.319, 0.319, 0.282, 0.282, 
0.396, 0.396, 0.301, 0.301, 0.841, 0.841, 0.335, 
0.335, 0.514, 0.514, 0.332, 0.332, 0.454, 0.454, 
0.380, 0.380, 0.528, 0.528, 0.301, 0.301, 0.403, 
0.403, 0.540, 0.540, 0.384, 0.384, 0.692, 0.692, 
0.340, 0.340, 0.355, 0.355, 0.358, 0.358, 0.306, 
0.306, 0.354, 0.354, 0.280, 0.280, 0.309, 0.309, 
0.727, 0.727, 0.304, 0.304, 0.432, 0.432, 0.307, 
0.307, 0.412, 0.412, 0.287, 0.287, 0.322, 0.322, 
0.395, 0.395, 0.284, 0.284, 0.269, 0.269, 0.509, 
0.509, 0.393, 0.393, 0.351, 0.351, 0.291, 0.291, 
0.439, 0.439, 0.315, 0.315, 0.357, 0.357, 0.312, 
0.312, 0.444, 0.444, 0.398, 0.398, 0.519, 0.519, 
0.334, 0.334, 0.567, 0.567, 0.276, 0.276, 0.392, 
0.392, 0.428, 0.428, 0.333, 0.333, 0.279, 0.279, 
0.314, 0.314, 0.297, 0.297, 0.366, 0.366, 0.317, 
0.317, 0.437, 0.437, 0.410, 0.410, 0.397, 0.397, 
0.581, 0.581, 0.518, 0.518, 0.344, 0.344, 0.516, 
0.516, 0.329, 0.329, 0.365, 0.365, 0.437, 0.437, 
0.473, 0.473, 0.434, 0.434, 0.368, 0.368, 0.356, 
0.356, 0.881, 0.881, 0.317, 0.317, 0.299, 0.299, 
0.266, 0.266, 0.329, 0.329, 0.357, 0.357, 0.312, 
0.312, 0.339, 0.339, 0.291, 0.291, 0.373, 0.373, 
0.312, 0.312, 0.352, 0.352, 0.661, 0.661, 0.332, 
0.332, 0.419, 0.419, 0.512, 0.512, 0.290, 0.290, 
0.434, 0.434, 0.491, 0.491, 0.318, 0.318, 0.495, 
0.495, 0.354, 0.354, 0.652, 0.652, 0.373, 0.373, 
0.279, 0.279, 0.274, 0.274, 0.359, 0.359, 0.330, 
0.330, 0.271, 0.271, 0.260, 0.260, 0.398, 0.398, 
0.275, 0.275, 0.378, 0.378, 0.402, 0.402, 0.302, 
0.302, 0.395, 0.395, 0.306, 0.306, 0.326, 0.326, 
0.350, 0.350, 0.382, 0.382, 0.329, 0.329, 0.329, 
0.329, 0.334, 0.334, 0.312, 0.312, 0.367, 0.367, 
0.286, 0.286, 0.671, 0.671, 0.615, 0.615, 0.323, 
0.323, 0.337, 0.337, 0.392, 0.392, 0.576, 0.576, 
0.405, 0.405, 0.317, 0.317, 0.394, 0.394, 0.436, 
0.436, 0.392, 0.392, 0.352, 0.352, 0.377, 0.377, 
0.419, 0.419, 0.461, 0.461, 0.303, 0.303, 0.358, 
0.358, 0.466, 0.466, 0.316, 0.316, 0.574, 0.574, 
0.525, 0.525, 0.301, 0.301, 0.648, 0.648, 0.622, 
0.622, 0.331, 0.331, 0.365, 0.365, 0.461, 0.461, 
0.386, 0.386, 0.343, 0.343, 0.765, 0.765, 0.318, 
0.318, 0.298, 0.298, 0.391, 0.391, 0.332, 0.332, 
0.343, 0.343, 0.359, 0.359, 0.403, 0.403, 0.368, 
0.368, 0.645, 0.645, 0.319, 0.319, 0.349, 0.349, 
0.344, 0.344, 0.307, 0.307, 0.332, 0.332, 0.383, 
0.383, 0.367, 0.367, 0.472, 0.472, 0.373, 0.373, 
0.336, 0.336, 0.304, 0.304, 0.280, 0.280, 0.389, 
0.389, 0.449, 0.449, 0.479, 0.479, 0.279, 0.279, 
0.255, 0.255, 0.241, 0.241, 0.473, 0.473, 0.526, 
0.526, 0.549, 0.549, 0.393, 0.393, 0.331, 0.331, 
0.412, 0.412, 0.324, 0.324, 0.538, 0.538, 0.340, 
0.340, 0.327, 0.327, 0.625, 0.625, 0.348, 0.348, 
0.388, 0.388, 0.289, 0.289, 0.392, 0.392, 0.539, 
0.539, 0.667, 0.667, 0.404, 0.404, 0.230, 0.230, 
0.336, 0.336, 0.370, 0.370, 0.309, 0.309, 0.744, 
0.744, 0.352, 0.352, 0.543, 0.543, 0.350, 0.350, 
0.390, 0.390, 0.581, 0.581, 0.344, 0.344, 0.320, 
0.320, 0.296, 0.296, 0.605, 0.605, 0.351, 0.351, 
0.383, 0.383, 0.336, 0.336, 0.376, 0.376, 0.314, 
0.314, 0.352, 0.352, 0.278, 0.278, 0.364, 0.364, 
0.369, 0.369, 0.335, 0.335, 0.366, 0.366, 0.650, 
0.650, 0.401, 0.401, 0.357, 0.357, 0.323, 0.323, 
0.381, 0.381, 0.371, 0.371, 0.388, 0.388, 0.321, 
0.321, 0.527, 0.527, 0.538, 0.538, 0.395, 0.395, 
0.320, 0.320, 0.358, 0.358, 0.341, 0.341, 0.750, 
0.750, 0.750, 0.750, 0.393, 0.393, 0.345, 0.345, 
0.349, 0.349, 0.615, 0.615, 0.291, 0.291, 0.311, 
0.311, 0.256, 0.256, 0.323, 0.323, 0.344, 0.344, 
0.351, 0.351, 0.482, 0.482, 0.595, 0.595, 0.338, 
0.338, 0.319, 0.319, 0.401, 0.401, 0.356, 0.356, 
0.314, 0.314, 0.371, 0.371, 0.437, 0.437, 0.393, 
0.393, 0.328, 0.328, 0.341, 0.341, 0.436, 0.436, 
0.697, 0.697, 0.433, 0.433, 0.345, 0.345, 0.455, 
0.455, 0.382, 0.382, 0.428, 0.428, 0.344, 0.344, 
0.334, 0.334, 0.339, 0.339, 0.347, 0.347, 0.351, 
0.351, 0.309, 0.309, 0.283, 0.283, 0.353, 0.353, 
0.291, 0.291, 0.312, 0.312, 0.345, 0.345, 0.301, 
0.301, 0.302, 0.302, 0.327, 0.327, 0.249, 0.249, 
0.391, 0.391, 0.336, 0.336, 0.355, 0.355, 0.399, 
0.399, 0.342, 0.342, 0.333, 0.333, 0.374, 0.374, 
0.273, 0.273, 0.324, 0.324, 0.531, 0.531, 0.267, 
0.267, 0.333, 0.333, 0.282, 0.282, 0.292, 0.292, 
0.397, 0.397, 0.332, 0.332, 0.327, 0.327, 0.342, 
0.342, 0.231, 0.231, 0.282, 0.282, 0.372, 0.372, 
0.341, 0.341, 0.327, 0.327, 0.356, 0.356, 0.308, 
0.308, 0.337, 0.337, 0.486, 0.486, 0.330, 0.330, 
0.419, 0.419, 0.282, 0.282, 0.407, 0.407, 0.442, 
0.442, 0.289, 0.289, 0.460, 0.460, 0.325, 0.325, 
0.424, 0.424, 0.312, 0.312, 0.395, 0.395, 0.317, 
0.317, 0.318, 0.318, 0.541, 0.541, 0.298, 0.298, 
0.433, 0.433, 0.374, 0.374, 0.439, 0.439, 0.299, 
0.299, 0.330, 0.330, 0.316, 0.316, 0.357, 0.357, 
0.373, 0.373, 0.320, 0.320, 0.299, 0.299, 0.300, 
0.300, 0.314, 0.314, 0.363, 0.363, 0.311, 0.311, 
0.309, 0.309, 0.305, 0.305, 0.368, 0.368, 0.330, 
0.330, 0.330, 0.330, 0.306, 0.306, 0.397, 0.397, 
0.294, 0.294, 0.315, 0.315, 0.300, 0.300, 0.318, 
0.318, 0.316, 0.316, 0.536, 0.536, 0.530, 0.530, 
0.382, 0.382, 0.425, 0.425, 0.562, 0.562, 0.714, 
0.714, 0.344, 0.344, 0.404, 0.404, 0.349, 0.349, 
0.343, 0.343, 0.359, 0.359, 0.334, 0.334, 0.353, 
0.353, 0.382, 0.382, 0.495, 0.495, 0.308, 0.308, 
0.661, 0.661, 0.372, 0.372, 0.324, 0.324, 0.333, 
0.333, 0.800, 0.800, 0.281, 0.281, 0.481, 0.481, 
0.277, 0.277, 0.346, 0.346, 0.433, 0.433, 0.491, 
0.491, 0.336, 0.336, 0.351, 0.351, 0.408, 0.408, 
0.750, 0.750, 0.481, 0.481, 0.408, 0.408, 0.355, 
0.355, 0.406, 0.406, 0.313, 0.313, 0.524, 0.524, 
0.781, 0.781, 0.357, 0.357, 0.303, 0.303, 0.311, 
0.311, 0.354, 0.354, 0.451, 0.451, 0.305, 0.305, 
0.288, 0.288, 0.630, 0.630, 0.296, 0.296, 0.431, 
0.431, 0.346, 0.346, 0.331, 0.331, 0.791, 0.791, 
0.638, 0.638, 0.288, 0.288, 0.340, 0.340, 0.432, 
0.432, 0.289, 0.289, 0.295, 0.295, 0.722, 0.722, 
0.299, 0.299, 0.309, 0.309, 0.381, 0.381, 0.303, 
0.303, 0.294, 0.294, 0.390, 0.390, 0.307, 0.307, 
0.409, 0.409, 0.372, 0.372, 0.500, 0.500, 0.360, 
0.360, 0.322, 0.322, 0.418, 0.418, 0.349, 0.349, 
0.335, 0.335, 0.398, 0.398, 0.726, 0.726, 0.417, 
0.417, 0.444, 0.444, 0.319, 0.319, 0.370, 0.370, 
0.378, 0.378, 0.556, 0.556, 0.609, 0.609, 0.329, 
0.329, 0.347, 0.347, 0.340, 0.340, 0.462, 0.462, 
0.337, 0.337, 0.553, 0.553, 0.502, 0.502, 0.622, 
0.622, 0.343, 0.343, 0.404, 0.404, 0.449, 0.449, 
0.265, 0.265, 0.486, 0.486, 0.485, 0.485, 0.382, 
0.382, 0.332, 0.332, 0.300, 0.300, 0.500, 0.500, 
0.600, 0.600, 0.334, 0.334, 0.349, 0.349, 0.430, 
0.430, 0.344, 0.344, 0.442, 0.442, 0.477, 0.477, 
0.615, 0.615, 0.398, 0.398, 0.677, 0.677, 0.309, 
0.309, 0.288, 0.288, 0.388, 0.388, 0.313, 0.313, 
0.274, 0.274, 0.295, 0.295, 0.757, 0.757, 0.467, 
0.467, 0.392, 0.392, 0.610, 0.610, 0.479, 0.479, 
0.550, 0.550, 0.393, 0.393, 0.367, 0.367, 0.580, 
0.580, 0.280, 0.280, 0.332, 0.332, 0.372, 0.372, 
0.553, 0.553, 0.370, 0.370, 0.291, 0.291, 0.514, 
0.514, 0.331, 0.331, 0.359, 0.359, 0.406, 0.406, 
0.364, 0.364, 0.542, 0.542, 0.335, 0.335, 0.568, 
0.568, 0.295, 0.295, 0.325, 0.325, 0.308, 0.308, 
0.489, 0.489, 0.308, 0.308, 0.306, 0.306, 0.328, 
0.328, 0.405, 0.405, 0.486, 0.486, 0.378, 0.378, 
0.359, 0.359, 0.422, 0.422, 0.596, 0.596, 0.565, 
0.565, 0.698, 0.698, 0.456, 0.456, 0.357, 0.357, 
0.686, 0.686, 0.535, 0.535, 0.425, 0.425, 0.453, 
0.453, 0.350, 0.350, 0.424, 0.424, 0.311, 0.311, 
0.376, 0.376, 0.581, 0.581, 0.296, 0.296, 0.350, 
0.350, 0.259, 0.259, 0.325, 0.325, 0.642, 0.642, 
0.532, 0.532, 0.526, 0.526, 0.450, 0.450, 0.362, 
0.362, 0.380, 0.380, 0.481, 0.481, 0.323, 0.323, 
0.326, 0.326, 0.341, 0.341, 0.633, 0.633, 0.789, 
0.789, 0.435, 0.435, 0.384, 0.384, 0.587, 0.587, 
0.406, 0.406, 0.507, 0.507, 0.323, 0.323, 0.431, 
0.431, 0.332, 0.332, 0.357, 0.357, 0.368, 0.368, 
0.240, 0.240, 0.431, 0.431, 0.353, 0.353, 0.414, 
0.414, 0.241, 0.241, 0.424, 0.424, 0.469, 0.469, 
0.363, 0.363, 0.298, 0.298, 0.378, 0.378, 0.648, 
0.648, 0.520, 0.520, 0.476, 0.476, 0.553, 0.553, 
0.283, 0.283, 0.366, 0.366, 0.396, 0.396, 0.294, 
0.294, 0.282, 0.282, 0.349, 0.349, 0.339, 0.339, 
0.350, 0.350, 0.462, 0.462, 0.338, 0.338, 0.329, 
0.329, 0.484, 0.484, 0.414, 0.414, 0.481, 0.481, 
0.295, 0.295, 0.299, 0.299, 0.683, 0.683, 0.290, 
0.290, 0.438, 0.438, 0.458, 0.458, 0.278, 0.278, 
0.583, 0.583, 0.339, 0.339, 0.404, 0.404, 0.297, 
0.297, 0.462, 0.462, 0.391, 0.391, 0.571, 0.571, 
0.370, 0.370, 0.346, 0.346, 0.461, 0.461, 0.359, 
0.359, 0.317, 0.317, 0.374, 0.374, 0.294, 0.294, 
0.326, 0.326, 0.336, 0.336, 0.339, 0.339, 0.328, 
0.328, 0.522, 0.522, 0.596, 0.596, 0.271, 0.271, 
0.355, 0.355, 0.466, 0.466, 0.353, 0.353, 0.446, 
0.446, 0.384, 0.384, 0.356, 0.356, 0.340, 0.340, 
0.379, 0.379, 0.500, 0.500, 0.487, 0.487, 0.442, 
0.442, 0.303, 0.303, 0.368, 0.368, 0.373, 0.373, 
0.323, 0.323, 0.421, 0.421, 0.363, 0.363, 0.229, 
0.229, 0.414, 0.414, 0.435, 0.435, 0.402, 0.402, 
0.345, 0.345, 0.413, 0.413, 0.446, 0.446, 0.303, 
0.303, 0.345, 0.345, 0.382, 0.382, 0.350, 0.350, 
0.409, 0.409, 0.416, 0.416, 0.367, 0.367, 0.407, 
0.407, 0.353, 0.353, 0.288, 0.288, 0.406, 0.406, 
0.396, 0.396, 0.440, 0.440, 0.385, 0.385, 0.416, 
0.416, 0.326, 0.326, 0.331, 0.331, 0.398, 0.398, 
0.446, 0.446, 0.442, 0.442, 0.454, 0.454, 0.404, 
0.404, 0.428, 0.428, 0.377, 0.377, 0.345, 0.345, 
0.404, 0.404, 0.313, 0.313, 0.297, 0.297, 0.443, 
0.443, 0.342, 0.342, 0.412, 0.412, 0.453, 0.453, 
0.380, 0.380, 0.314, 0.314, 0.396, 0.396, 0.569, 
0.569, 0.321, 0.321, 0.376, 0.376, 0.526, 0.526, 
0.422, 0.422, 0.350, 0.350, 0.341, 0.341, 0.446, 
0.446, 0.367, 0.367, 0.382, 0.382, 0.356, 0.356, 
0.428, 0.428, 0.392, 0.392, 0.392, 0.392, 0.367, 
0.367, 0.371, 0.371, 0.411, 0.411, 0.443, 0.443, 
0.383, 0.383, 0.400, 0.400, 0.430, 0.430, 0.404, 
0.404, 0.429, 0.429, 0.505, 0.505, 0.443, 0.443, 
0.319, 0.319, 0.450, 0.450, 0.345, 0.345, 0.309, 
0.309, 0.362, 0.362, 0.444, 0.444, 0.414, 0.414, 
0.475, 0.475, 0.467, 0.467, 0.359, 0.359, 0.327, 
0.327, 0.473, 0.473, 0.320, 0.320, 0.318, 0.318, 
0.288, 0.288, 0.399, 0.399, 0.300, 0.300, 0.343, 
0.343, 0.381, 0.381, 0.436, 0.436, 0.303, 0.303, 
0.377, 0.377, 0.468, 0.468, 0.383, 0.383, 0.317, 
0.317, 0.438, 0.438, 0.485, 0.485, 0.389, 0.389, 
0.332, 0.332, 0.310, 0.310, 0.307, 0.307, 0.435, 
0.435, 0.385, 0.385, 0.402, 0.402, 0.433, 0.433, 
0.580, 0.580, 0.405, 0.405, 0.391, 0.391, 0.356, 
0.356, 0.486, 0.486, 0.385, 0.385, 0.391, 0.391, 
0.540, 0.540, 0.346, 0.346, 0.327, 0.327, 0.306, 
0.306, 0.419, 0.419, 0.431, 0.431, 0.458, 0.458, 
0.442, 0.442, 0.419, 0.419, 0.374, 0.374, 0.306, 
0.306, 0.347, 0.347, 0.468, 0.468, 0.367, 0.367, 
0.496, 0.496, 0.587, 0.587, 0.444, 0.444, 0.487, 
0.487, 0.540, 0.540, 0.420, 0.420, 0.325, 0.325, 
0.455, 0.455, 0.515, 0.515, 0.475, 0.475, 0.698, 
0.698, 0.471, 0.471, 0.474, 0.474, 0.328, 0.328, 
0.533, 0.533, 0.426, 0.426, 0.385, 0.385, 0.545, 
0.545, 0.404, 0.404, 0.509, 0.509, 0.500, 0.500, 
0.439, 0.439, 0.347, 0.347, 0.519, 0.519, 0.434, 
0.434, 0.410, 0.410, 0.314, 0.314, 0.449, 0.449, 
0.336, 0.336, 0.419, 0.419, 0.422, 0.422, 0.346, 
0.346, 0.449, 0.449, 0.407, 0.407, 0.392, 0.392, 
0.323, 0.323, 0.320, 0.320, 0.526, 0.526, 0.426, 
0.426, 0.557, 0.557, 0.569, 0.569, 0.577, 0.577, 
0.346, 0.346, 0.509, 0.509, 0.388, 0.388, 0.341, 
0.341, 0.472, 0.472, 0.352, 0.352, 0.424, 0.424, 
0.338, 0.338, 0.404, 0.404, 0.450, 0.450, 0.359, 
0.359, 0.531, 0.531, 0.384, 0.384, 0.348, 0.348, 
0.527, 0.527, 0.605, 0.605, 0.496, 0.496, 0.368, 
0.368, 0.343, 0.343, 0.500, 0.500, 0.469, 0.469, 
0.346, 0.346, 0.408, 0.408, 0.437, 0.437, 0.350, 
0.350, 0.433, 0.433, 0.434, 0.434, 0.415, 0.415, 
0.442, 0.442, 0.495, 0.495, 0.660, 0.660, 0.430, 
0.430, 0.610, 0.610, 0.586, 0.586, 0.481, 0.481, 
0.442, 0.442, 0.506, 0.506, 0.424, 0.424, 0.544, 
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0.340, 0.305, 0.305, 0.276, 0.276, 0.612, 0.612, 
0.275, 0.275, 0.295, 0.295, 0.310, 0.310, 0.353, 
0.353, 0.453, 0.453, 0.296, 0.296, 0.280, 0.280, 
0.385, 0.385, 0.407, 0.407, 0.246, 0.246, 0.278, 
0.278, 0.257, 0.257, 0.257, 0.257, 0.345, 0.345, 
0.349, 0.349, 0.284, 0.284, 0.274, 0.274, 0.295, 
0.295, 0.279, 0.279, 0.262, 0.262, 0.372, 0.372, 
0.334, 0.334, 0.262, 0.262, 0.348, 0.348, 0.281, 
0.281, 0.307, 0.307, 0.247, 0.247, 0.246, 0.246, 
0.448, 0.448, 0.318, 0.318, 0.260, 0.260, 0.271, 
0.271, 0.346, 0.346, 0.487, 0.487, 0.319, 0.319, 
0.348, 0.348, 0.350, 0.350, 0.258, 0.258, 0.292, 
0.292, 0.244, 0.244, 0.284, 0.284, 0.376, 0.376, 
0.325, 0.325, 0.263, 0.263, 0.417, 0.417, 0.614, 
0.614, 0.270, 0.270, 0.231, 0.231, 0.528, 0.528, 
0.381, 0.381, 0.325, 0.325, 0.285, 0.285, 0.449, 
0.449, 0.379, 0.379, 0.249, 0.249, 0.278, 0.278, 
0.332, 0.332, 0.414, 0.414, 0.275, 0.275, 0.429, 
0.429, 0.318, 0.318, 0.270, 0.270, 0.564, 0.564, 
0.249, 0.249, 0.337, 0.337, 0.346, 0.346, 0.455, 
0.455, 0.286, 0.286, 0.403, 0.403, 0.413, 0.413, 
0.240, 0.240, 0.268, 0.268, 0.283, 0.283, 0.277, 
0.277, 0.243, 0.243, 0.568, 0.568, 0.314, 0.314, 
0.471, 0.471, 0.328, 0.328, 0.271, 0.271, 0.286, 
0.286, 0.260, 0.260, 0.265, 0.265, 0.313, 0.313, 
0.323, 0.323)

The code

quartiles <- quantile(x, probs = c(0, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5, 1))
symbols <- c("Q1", "Q2", "Q3", "Q4", "Q5", "Q6", "Q7")
x2 <- cut(x, breaks = quartiles, labels = symbols, include.lowest = TRUE)
table(x2)

produces

  Q1   Q2   Q3   Q4   Q5   Q6   Q7 
1010  204  180  190  194  222 1951

The why the command

length(x[x<=0.25])

returns the result 127, which is very different from 1010 obtained for Q1 class with quantile and cut?

EDIT

This is the histogram of the numeric variable x.

I obtained

>range(x[x2 == "Q1"])
[1] 0.188 0.303

and

length(x[x<=0.303])

returns 1010. It seems than that Q1 is the class associated to x<=0.303 and not to x<=0.25 as specified by the field probs = c(0, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5, 1) in the quantile argument. I mean to say that with this field, I intended to assign Q1 to numbers between 0 and 0.25, Q2 to numbers between 0.25 and 0.3, and so on. What am I doing wrong?

Answer 1

From ?quantile: The generic function quantile produces sample quantiles corresponding to the given probabilities. The smallest observation corresponds to a probability of 0 and the largest to a probability of 1.

So quantile(x, probs = 0.25) is asking for the 25th percentile of your data's distribution, not the values under 0.25. Skip it and use your probs breakpoints directly in cut() if you want to know how your data compares to those values.

probs = c(0, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5, 1)
symbols <- c("Q1", "Q2", "Q3", "Q4", "Q5", "Q6", "Q7")
x2 <- cut(x, breaks = probs, labels = symbols, include.lowest = TRUE)

table(x2)
#x2
#Q1   Q2   Q3   Q4   Q5   Q6   Q7 
#54  552 1082  742  604  390  526 

length(x[x<=0.25])
[1] 54  # This matches the size of Q1 above

length(x[x<=0.3])
[1] 606  # This matches Q1+Q2 above: 54 + 552 = 606