The Rise of Statistical Thinking, 1820-1900 by Theodore M. Porter
The Rise of Statistical Thinking emphasizes the commitment of science to ordinary intellectuals. The author explains the background of the 19th century which caused the outburst of statistical innovations.
In the same vein as the above, you could read "The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century" by David Salzburg, which is an effortless read.