In the histogram, the abscissa of the middle value of the small rectangle with the highest height is the mode.
According to the histogram of frequency distribution, the mode of mathematics score in this test is 75.
(2) Since the median is the middle value of all data,
Therefore, in the histogram, it is reflected that the frequencies on the left and right sides of the median are equal, that is, the frequencies are equal.
So that the sum of the areas of the small rectangles is equal,
Therefore, in the frequency distribution histogram,
The result corresponding to the straight line bisecting all the small rectangular areas in the histogram of frequency distribution is the demand.
∫ The sum of the areas of the first three small rectangles is (0.005+0.015+0.020) ×10 = 0.4.
The area of the fourth small rectangle is 0.030× 10=0.3, 0.4+0.3 = 0.7 > 0.5,
∴: The middle value should be in the fourth small rectangle.
Let its base be x and its height be 0.03.
∴ Let 0.03x=0. 1 and get x = 103 = 3 13.
So the median score is 7313;
(3) The average value is the "center of gravity" of the frequency distribution histogram,
It is equal to the sum of the areas of each small rectangle multiplied by the abscissa of the midpoint at the bottom of the small rectangle in the frequency distribution histogram.
So the average score is:
45×(0.005× 10)+55×(0.0 15× 10)+65×(0.020× 10)+
75×(0.030× 10)+85×(0.025× 10)+95×(0.005× 10)=72.
The average score is 72.