(a)
Q1, the first quartile, 25th percentile, is greater than or equal to 1/4 of the points. It's in the first bar so we can estimate Q1=5. In reality the bar includes values from 0 to 9 or 10 (not clear which) and has around 37% of the points so we might estimate Q1 a bit higher as it's 2/3 of the points, say Q1=7.
The median is bigger than half the points. First bar is 37%, next is 22%, so its about halfway in the second bar, median=15
Third bar is 11%, so 70% so far. Four bar is 5%, so we're at the right end of the fourth bar for Q3, the third quartile, 75th percentile, say Q3=40
b
When the data is heavily skewed left like it is here, the median tends to be lower than the mean. The 5% of the data from 80 to 120 averages around 100 so adds 5 to the mean, and 8% of the data from the 60 to 80 adds another 5.6, 15% of the data from 40 to 60 adds about 7.5, plus the rest, so the mean is gonna be way bigger than the median of around 15.
The answer would be because
All you gotta do is pick a random point on the x-axis, lets say, x=2 in this case, and plug it into the equation.
If x=2, y = (1/2)2 - 3 = 2 - 3 = -1
When x = 2, y = -1
Now pick another point, x = 1
x = 1, y = (1/2)1 - 3 = 0.5 - 3 = - 2.5
When x = 1, y = - 2.5
Draw a cross on those 2 points, on the 2d plane
(1, -2.5) and (2, -1)
and draw a line between them, and make the line continue past the points, having no boundaries but the paper you hold, keeping it straight the entire time. With not turns.
If you want to draw out a table, make it have 2 rows, and 6 columns.
Write x in the first column of the first row, and write y in the first column of the second row.
Now, write down a different, random x value, in each column in the first row.
In the second row, in each column, write the y value, that corresponds to the x value given above each individual column, based on the equation
y = 1/2x - 3.
70 miles apart :)
hope I helped :) If you want work shown comment of this please :)
The slope of the tangent at a given point can be found by differentiating the given equation and substituting the value of x at the point as such:
y = 9 - x²
dy/dx = -2x; x = 1
dy/dx = -2
For a line with the slope of -2 and passing through point (1 , 12)
y -12 = -2(x - 1)
