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Numerade Educator



Problem 39 Hard Difficulty

An approximate median can be found for data that have been grouped into a frequency distribution. First it is necessary to find the median class. This is the class that contains the median value. That is the n/2 data value. Then it is assumed that the data values are evenly distributed throughout the median class. The formula is
$$\mathrm{MD}=\frac{n / 2-\mathrm{cf}}{f}(w)+L_{m}$$
$\begin{aligned} \text { where } & n=\text { sum of frequencies } \\ & \mathrm{cf}=\text { cumulative frequency of class immedi- } \\ & \text { ately preceding the median class } \end{aligned}$
$$\begin{aligned} w &=\text { width of median class } \\ f &=\text { frequency of median class } \\ L_{m} &=\text { lower boundary of median class } \end{aligned}$$
Using this formula, find the median for data in the frequency distribution of Exercise $16 .$




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Video Transcript

problem. We are given a new formula for the median of a grouped data set on and were asked to use the data from the foreign born population for each state from number 16. So here's back data on and then this formula is ah lot. So here's what each, um, letter represents. So and we have our number and are frequent seats. So remember our frequency. All we need to do is add everything. I mean, we're talking about the number of foreign born people for each state. So when we out all of this 26 plus 11 plus four plus five plus two plus one plus one on, we should get 50. So here, we know are in is 15 then CF. Here is the cumulative frequency of the class immediately preceding the median class. So we need to figure out what the median class is. Um, and we do that by, um, using 50 and dividing it by two. So a median class will be 50 divided by two, which will give us 25. So then whichever frequency has this number included on, then that will be our class. So our median class is this 1st 1.8 to 4.4. Um and so are cumulative frequency of the class immediately preceding the median cross. Well, we don't have a class before 0.8 to 4.4, so this value is going to be zero on. Then we want the width of our median class. So all we have to do is 4.4, minus 2.8, and we will get 3.6, and then our frequency of the median class is right here. We know that is 26 and then we want the lower bound for our median class, and that is 0.8. So once we recognized each of these values, all we need to do is play it into our formula. So here we're gonna have that the median MD equals. We know that our in is 50. So offifty, divided by two minus zero, divided by R value of F, which is 26. And then we're gonna multiply this by our with of 3.6 and we're subtracting or sorry. We're adding, are lower bound of zero point eight. And when we playing all of those values in, we will get a median for a groups data of 4.26