![]() The lower quartile, or first quartile (Q1), is the value under which 25% of data points are found when they are arranged in increasing order. To calculate these two measures, you need to know the values of the lower and upper quartiles. The interquartile range and semi-interquartile range give a better idea of the dispersion of data. ![]() It's used as a supplement to other measures, but it is rarely used as the sole measure of dispersion because it’s sensitive to extreme values. The range only takes into account these two values and ignore the data points between the two extremities of the distribution. Of 20.408 m, then h decreases again to zero, as expected.To calculate the range, you need to find the largest observed value of a variable (the maximum) and subtract the smallest observed value (the minimum). `t = -b/(2a) = -20/(2 xx (-4.9)) = 2.041 s `īy observing the function of h, we see that as t increases, h first increases to a maximum ![]() ![]() What is the maximum value of h? We use the formula for maximum (or minimum) of a quadratic function. It goes up to a certain height and then falls back down.) (This makes sense if you think about throwing a ball upwards. We can see from the function expression that it is a parabola with its vertex facing up. So we need to calculate when it is going to hit the ground. Also, we need to assume the projectile hits the ground and then stops - it does not go underground. Generally, negative values of time do not have any Have a look at the graph (which we draw anyway to check we are on the right track): So we can conclude the range is `(-oo,0]uu(oo,0)`. We have `f(-2) = 0/(-5) = 0.`īetween `x=-2` and `x=3`, `(x^2-9)` gets closer to `0`, so `f(x)` will go to `-oo` as it gets near `x=3`.įor `x>3`, when `x` is just bigger than `3`, the value of the bottom is just over `0`, so `f(x)` will be a very large positive number.įor very large `x`, the top is large, but the bottom will be much larger, so overall, the function value will be very small. As `x` increases value from `-2`, the top will also increase (out to infinity in both cases).ĭenominator: We break this up into four portions: To work out the range, we consider top and bottom of the fraction separately. So the domain for this case is `x >= -2, x != 3`, which we can write as `[-2,3)uu(3,oo)`. (Usually we have to avoid 0 on the bottom of a fraction, or negative values under the square root sign). In general, we determine the domain of each function by looking for those values of the independent variable (usually x) which we are allowed to use. For a more advanced discussion, see also How to draw y^2 = x − 2.
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