# Matplotlib.pyplot.hist: Why are these 2 'density' histograms not more alike?

According to my logic, these 2 ways of plotting histograms of my 2 datasets should look quite similar, both they look quite different. Why?

The first one is plotted with ‘density=True’, to compensate for the fact that one data set has the double number of values compared to the other:

The second is plotted with ‘density=False’, but I am halving the amount of values in one data set, so the 2 data sets have the same number of values:

This is the Python code for the 2 histograms:

``````from matplotlib import pyplot as plot

plot.hist((sw_sums, ww_sums), edgecolor='black', bins=hist_plot_bins, density=True)
plot.title("Substance-Water vs. Water-Water FFT frequency spectrum sums. {} bins.".format(hist_plot_bins))
plot.legend(["Substance-Water, {} data points.".format(len(sw_sums)) ,"Water-Water, {} data points.".format(len(ww_sums))])
plot.xlabel('FFT sum')
plot.ylabel('density=True')
plot.grid()
plot.show()

# Since sw_sums has the double amount of elements compared to ww_sums, I average 2 at a time:
sw_sums.sort()
new_sw_sums = []
for i in range(0, len(sw_sums), 2):
new_sw_sums.append((sw_sums[i]+sw_sums[i+1])/2)
plot.hist((new_sw_sums, ww_sums), edgecolor='black', bins=hist_plot_bins, density=False)
plot.title("Substance-Water vs. Water-Water FFT frequency spectrum sums. {} bins.".format(hist_plot_bins))
plot.legend(["Substance-Water, {} data points.".format(len(new_sw_sums)) ,"Water-Water, {} data points.".format(len(ww_sums))])
plot.xlabel('FFT sum')
plot.ylabel('density=False')
plot.grid()
plot.show()
``````

Any explanation for the big difference between the 2 ‘density’ plots would be very appreciated. Thank you.

Here are the 2 data sets:

sw_sums= [‘-144,094.3’, ‘261,381.4’, ‘15,835.0’, ‘16,054.2’, ‘127,970.8’, ‘173,325.2’, ‘8,821.8’, ‘104,846.2’, ‘-273,515.6’, ‘-255,622.8’, ‘-182,685.4’, ‘20,458.2’, ‘-543,755.2’, ‘-329,407.9’, ‘76,067.9’, ‘-169,478.5’, ‘-169,259.3’, ‘-57,342.7’, ‘-11,988.3’, ‘-176,491.7’, ‘-80,467.3’, ‘-458,829.1’, ‘-440,936.4’, ‘-367,998.9’, ‘-164,855.3’, ‘-729,068.7’, ‘-86,308.5’, ‘319,167.3’, ‘73,620.9’, ‘73,840.1’, ‘185,756.7’, ‘231,111.1’, ‘66,607.7’, ‘162,632.1’, ‘-215,729.7’, ‘-197,837.0’, ‘-124,899.5’, ‘78,244.1’, ‘-485,969.3’, ‘-118,988.9’, ‘286,486.8’, ‘40,940.5’, ‘41,159.7’, ‘153,076.3’, ‘198,430.6’, ‘33,927.2’, ‘129,951.7’, ‘-248,410.2’, ‘-230,517.4’, ‘-157,579.9’, ‘45,563.7’, ‘-518,649.7’, ‘104,568.3’, ‘510,044.0’, ‘264,497.7’, ‘264,716.9’, ‘376,633.4’, ‘421,987.8’, ‘257,484.4’, ‘353,508.8’, ‘-24,853.0’, ‘-6,960.2’, ‘65,977.3’, ‘269,120.9’, ‘-295,092.6’, ‘-49,442.2’, ‘356,033.5’, ‘110,487.1’, ‘110,706.4’, ‘222,622.9’, ‘267,977.3’, ‘103,473.9’, ‘199,498.3’, ‘-178,863.5’, ‘-160,970.7’, ‘-88,033.3’, ‘115,110.3’, ‘-449,103.1’, ‘161,633.9’, ‘567,109.7’, ‘321,563.3’, ‘321,782.5’, ‘433,699.1’, ‘479,053.5’, ‘314,550.1’, ‘410,574.5’, ‘32,212.7’, ‘50,105.4’, ‘123,042.9’, ‘326,186.5’, ‘-238,026.9’, ‘-159,693.9’, ‘245,781.8’, ‘235.4’, ‘454.7’, ‘112,371.2’, ‘157,725.6’, ‘-6,777.8’, ‘89,246.6’, ‘-289,115.2’, ‘-271,222.4’, ‘-198,285.0’, ‘4,858.7’, ‘-559,354.8’, ‘130,789.1’, ‘536,264.8’, ‘290,718.4’, ‘290,937.7’, ‘402,854.2’, ‘448,208.6’, ‘283,705.2’, ‘379,729.6’, ‘1,367.8’, ‘19,260.6’, ‘92,198.0’, ‘295,341.6’, ‘-268,871.8’, ‘99,830.3’, ‘505,306.0’, ‘259,759.7’, ‘259,978.9’, ‘371,895.4’, ‘417,249.8’, ‘252,746.4’, ‘348,770.9’, ‘-29,591.0’, ‘-11,698.2’, ‘61,239.3’, ‘264,382.9’, ‘-299,830.6’, ‘-104,052.8’, ‘301,422.9’, ‘55,876.5’, ‘56,095.8’, ‘168,012.3’, ‘213,366.7’, ‘48,863.3’, ‘144,887.7’, ‘-233,474.1’, ‘-215,581.3’, ‘-142,643.9’, ‘60,499.7’, ‘-503,713.7’, ‘36,288.7’, ‘441,764.5’, ‘196,218.1’, ‘196,437.3’, ‘308,353.9’, ‘353,708.3’, ‘189,204.9’, ‘285,229.3’, ‘-93,132.5’, ‘-75,239.8’, ‘-2,302.3’, ‘200,841.3’, ‘-363,372.1’, ‘124,382.4’, ‘529,858.2’, ‘284,311.8’, ‘284,531.0’, ‘396,447.6’, ‘441,802.0’, ‘277,298.6’, ‘373,323.0’, ‘-5,038.8’, ‘12,853.9’, ‘85,791.4’, ‘288,935.0’, ‘-275,278.4’, ‘-51,917.2’, ‘353,558.6’, ‘108,012.2’, ‘108,231.4’, ‘220,148.0’, ‘265,502.4’, ‘100,999.0’, ‘197,023.4’, ‘-181,338.4’, ‘-163,445.7’, ‘-90,508.2’, ‘112,635.4’, ‘-451,578.0’]
ww_sums= [‘185,313.5’, ‘-57,785.9’, ‘-25,105.4’, ‘-248,662.6’, ‘-94,652.1’, ‘-305,728.3’, ‘15,599.6’, ‘-274,883.4’, ‘-243,924.6’, ‘-40,041.5’, ‘-180,383.1’, ‘-268,476.8’, ‘-92,177.2’, ‘-243,099.4’, ‘-210,419.0’, ‘-433,976.1’, ‘-279,965.6’, ‘-491,041.8’, ‘-169,713.9’, ‘-460,196.9’, ‘-429,238.1’, ‘-225,355.0’, ‘-365,696.6’, ‘-453,790.3’, ‘-277,490.7’, ‘32,680.4’, ‘-190,876.8’, ‘-36,866.2’, ‘-247,942.4’, ‘73,385.4’, ‘-217,097.5’, ‘-186,138.8’, ‘17,744.4’, ‘-122,597.2’, ‘-210,690.9’, ‘-34,391.3’, ‘-223,557.2’, ‘-69,546.7’, ‘-280,622.8’, ‘40,705.0’, ‘-249,778.0’, ‘-218,819.2’, ‘-14,936.1’, ‘-155,277.6’, ‘-243,371.3’, ‘-67,071.7’, ‘154,010.5’, ‘-57,065.6’, ‘264,262.2’, ‘-26,220.8’, ‘4,738.0’, ‘208,621.1’, ‘68,279.6’, ‘-19,814.1’, ‘156,485.4’, ‘-211,076.2’, ‘110,251.7’, ‘-180,231.3’, ‘-149,272.5’, ‘54,610.6’, ‘-85,730.9’, ‘-173,824.7’, ‘2,474.9’, ‘321,327.8’, ‘30,844.9’, ‘61,803.6’, ‘265,686.8’, ‘125,345.2’, ‘37,251.5’, ‘213,551.1’, ‘-290,483.0’, ‘-259,524.2’, ‘-55,641.1’, ‘-195,982.6’, ‘-284,076.3’, ‘-107,776.8’, ‘30,958.8’, ‘234,841.9’, ‘94,500.4’, ‘6,406.6’, ‘182,706.2’, ‘203,883.1’, ‘63,541.6’, ‘-24,552.1’, ‘151,747.4’, ‘-140,341.5’, ‘-228,435.2’, ‘-52,135.7’, ‘-88,093.7’, ‘88,205.9’, ‘176,299.6’]

These distributions look fairly similar to me. However, you might want to try setting `bins` to a sequence of bin edges instead of an integer. That way you will be using identical bins for both plots. If you pass an integer, Matplotlib works out the bin edges based on the range of your data, which you have reduced by averaging elements in the blue data set.

Great! Thank you. That helped a lot!

If I define the bin edges first and use those bins in both plots, then they look much more similar:

``````bins_edges = np.histogram_bin_edges(sw_sums, bins=hist_plot_bins)

plot.hist((sw_sums, ww_sums), edgecolor='black', bins=bins_edges, density=True)
``````

``````plot.hist((new_sw_sums, ww_sums), edgecolor='black', bins=bins_edges, density=False)
``````

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