create bins based on a range of values for histogram figure

Question

I am doing some analysis and need to produce a histogram plot. I know how to create the standard histogram plot but I need something like the image below, where each point is an interval on the x axis. Each bin is based on a value from x-x for example.

Answer 1

You can use the histogram function, and then set the XTick positions and XTickLabels accordingly. See the comments in the code for explanation.

% random normally distrubuted data
x = 1*randn(1000,1);
edges = -5:1:5;

% create vector with labels (for XTickLabel ... to ...)
labels = [edges(1:end-1); edges(2:end)];
labels = labels(:);

% plot the histogram
figure();
ax = axes;
h = histogram(x, 'BinEdges', edges, 'Normalization', 'Probability');

ax.XTick = edges + mean(diff(edges)/2);
ax.XTickLabel = sprintf('%.1f to %.1f\n', labels);
ax.XTickLabelRotation = 90;

% set yticks to percentage
ax.YTickLabel = cellfun(@(a) sprintf('%i%%', (str2double(a)*100)), ax.YTickLabel, 'UniformOutput', false);

% text above bars
bin_props = h.BinCounts/numel(x);  % determine probabilities per bin in axis units
bin_centers = ax.XTick(1:end-1);  % get the bin centers

txt_heigts = bin_props + 0.01; % put the text slightly above the bar
txt_labels = split(sprintf('%.1f%% ', bin_props*100), ' ');
txt_labels(end) = [];  % remove last cell, is empty because of split.
text(ax, bin_centers, txt_heigts, txt_labels, 'HorizontalAlignment', 'center')

% set ylim to fit all text (otherwise text is outside axes)
ylim([0 .4]);

Putting the text at the right location may require some tweaking. Most important is the 'HorizontalAlignment' option, and the distance to the bars. I also used the 'Normalization', 'probability' option from the histogram function, and set the y axis to also show percentages.

I figure you can make the addition below yourself when needed.

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When your data can be outside of the defined binedges, you can clip your data, and set the XTickLabels with less than or greater than signs.

% when data can be outside of defined edges
x = 5*randn(1000,1);
xclip = x;
xclip(x >= max(edges)) = max(edges);
xclip(x <= min(edges)) = min(edges);

% plot the histogram
figure();
ax = axes;
h = histogram(xclip, 'BinEdges', edges);

ax.XTick = edges + mean(diff(edges)/2);
ax.XTickLabel = sprintf('%.1f to %.1f\n', labels);
ax.XTickLabelRotation = 90;

% set boundary labels
ax.XTickLabel{1} = sprintf('\\leq %.1f', edges(2));
ax.XTickLabel{end-1} = sprintf('\\geq %.1f', edges(end-1));

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You can also set the outer edges to -Inf and Inf, as user2305193 pointed out. Since the outer bins are then much wider (because they actually extend to Inf on the x axis), which you can correct by setting the axis xlim. By the default the XTickLabels will display -Inf to -5.0, which I personally don't like, so I set them to lesser (and equal) than and greater than signs.

step = 1;
edges = -5:step:5;                                  % your defined range
edges_inf = [-Inf edges Inf];                       % for histogram
edges_ext = [edges(1)-step edges];                  % for the xticks

x = 5*randn(1000,1);

% plot the histogram
figure();
ax = axes;
h = histogram(x, 'BinEdges', edges_inf, 'Normalization', 'probability');

labels = [edges_inf(1:end-1); edges_inf(2:end)];
labels = labels(:);

ax.XTick = edges_ext + step/2;
ax.XTickLabel = sprintf('%.1f to %.1f\n', labels);
ax.XTickLabelRotation = 90;

% show all bins with equal width (Inf bins are in fact wider)
xlim([min(edges)-step max(edges)+step])

% set boundary labels
ax.XTickLabel{1} = sprintf('\\leq %.1f', edges(1));
ax.XTickLabel{end-1} = sprintf('\\geq %.1f', edges(end));