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Lots of things end up being normally distributed. Are Boston Marathon results one of them?

Let's try and find out if our data is normally distributed by seeing how many 0:00 finishers finished within one, two, and three standard deviations of the mean. 0:04 But first, we'll need to know how many finishers there were. 0:09 Let's add a row at the very top by right clicking on row 1 and 0:13 choosing insert 1 above. 0:16 Then let's add a label for number of finishers and make sure it's bold. 0:19 Then in cell B1, let's type =COUNT, 0:26 paste in our range of overall finish times, and hit Enter. 0:30 And there we go, 26,410 total finishers. 0:35 Getting back to our standard deviations, 0:41 let's add three labels below our standard deviation label, 0:45 and call them % in 1, % in 2, and % in 3. 0:52 And let's leave them unbolded so 0:57 they look like they belong with standard deviation, because they do. 0:59 Now, for % in 1, we need to find out haw many runners finished within 1 1:04 standard deviation of the mean. 1:09 To accomplish this, we're going to use the COUNTIFS function, which lets us give some 1:12 criteria and then only returns the count of values that match our criteria. 1:16 We're going to count only runners that finished within 1 standard deviation. 1:21 And then divide that by the total number of runners to get a percentage. 1:26 Over in cell B11, let's type =COUNTIFS and hit Enter to select it. 1:30 Then let's paste in the range of finishing times and add a comma. 1:39 The next parameter is the conditional statement. 1:43 And it's entered as a string. 1:46 So let's add two quotation marks and in the middle, let's add a greater than sign. 1:49 To find out if a runner is within 1 standard deviation of the mean, we need to 1:56 check that their finishing time is greater than the mean minus 1 standard deviation. 2:00 Unfortunately, this data exists in a cell. 2:07 So instead of typing the data in, we should reference the cell directly. 2:10 To do this, we need to combine our greater than sign 2:15 with our cell data by using an ampersand to concatenate the strings. 2:18 Let's add an ampersand after the last quotation mark. 2:23 Then let's select the average, type a minus sign and 2:27 then select the standard deviation. 2:31 We're now counting all runners greater than 1 standard deviation below the mean. 2:33 So to finish up counting all the runners within 1 standard deviation, we just need 2:40 to add a criteria that they finished under 1 standard deviation above the mean, 2:44 as well. 2:49 To do this, let's just copy the range and criteria that we just entered, 2:51 add a comma, and then paste them back in. 2:56 Finally, we just need to change this greater than sign to a less than sign, 3:00 and change this minus to a plus. 3:06 And add a closing parentheses. 3:11 For our last step, to turn this into a percentage we just need to divide it by 3:14 the total number of finishers. 3:19 Which gives us about 69.47%, 3:24 which is pretty close to the 68 of a normal distribution. 3:27 And to make it look like a percent, we can click up here and then choose percent. 3:34 From here, we can find our other standard deviation percentages pretty easily. 3:39 But first, let's use F4 to make all the references in this formula absolute. 3:43 This way, when we drag the cell down, it'll keep the same references. 3:50 Then let's drag the cell down twice. 4:03 And to get the % in 2 and 3, inside the formula for those cells, 4:08 we just need to multiply the standard deviation by 2 or 3 respectively. 4:13 And the standard deviation for me is this teal-colored B10. 4:19 So for % in 2, we'll multiply this by 2. 4:24 And over here we'll multiply it by 2. 4:28 And for % in 3 we'll do the same thing, except with 3. 4:32 All right, we've got 69.48, 4:41 94.91, and then 99.76%. 4:45 Remember, a normal distribution should be about 68% within 1 standard deviation, 4:50 95% within 2, and 99.7% within 3. 4:58 So it looks like the finishing times of runners in the Boston Marathon 5:02 are pretty close to normally distributed. 5:06 Coming up in the next video, 5:09 we'll talk about the many different flavors of data visualization. 5:10

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