So we're giving information for two different sets of data. And so let's call one set of data set one and information for the other set of data will be called set to. So range is defined as the maximum value in the data set of mine is the minimum value in the data set for So for the first day to set the maximum value Is 6.10 minutes. And for the other data for this dataset. Also The minimum time is 0.38 minutes for the other day to set the maximum value Is equivalent to 10.49 minutes. We'll have a minimum value Is given by 3.82 minutes. So you can find that the range first at one is Is equivalent to 5.72 minutes while the range were sent to is equivalent to 6.67 minutes. And really the only conclusion you can really draw from the range of the data is that there's really a greater for the second set of data there is essentially a greater difference between the maximum and minimum values. Branch isn't often the most particularly useful set of data since basically it's only also it's if you're only given the range and you're not given the maximum and minimum values range isn't particularly useful. Us US parameter basically to interpret. So mean is defined as the sum of everything in the data set divided by the number of elements in the data set. So for set one, if you plug everything into the one very little stats function, you can find that the mean is approximately, so you find that the mean for set one is equivalent to 3.88 minutes. While the mean first step to similarly using one variable Stassi in or plugging in Basically directly into the formula is equivalent to 7.02 minutes. So you can see here that there is essentially a significant difference, significant difference between the waiting times of basically these two sets of data, to be conclusively sure though that there is a significant difference between the two sets of data. Technically you would have to run a two sample T test, but just by eyeballing it, there seems to be a significant difference in the waiting time based on the mean of the of the two different sets of data. However, it's also important to remember that essentially mean can be easily skewed to the right or skewed to the left by different sets of outliers. So we have to be careful, especially with mean and often the median is a better way of approximating. So in this case were also asked for the sample standard deviation and in this case we're using specifically the sample standard deviation rather than the population standard deviation, Since we're only given basically a subset of the basically the total number of customers that enter basically this location. So the sample standard deviation for the first set of data is equivalent to Equals 1.55 minutes. While the sample standard deviation for the second step of data is equivalent to 2.24 minutes. So the sample standard deviation gives us a very good idea of basically the variability of data and since basically set to has a larger sample standard deviation, essentially this implies that there's typically greater variation in data for basically the second step second, basically the second set of data. And we're also asked to find the coefficient of basically the coefficient of variability mhm which is typically defined as this population standard deviation over the population means. But in this case, since we're treating a sample, we have the sample values. So the coefficient will just call in this case we can call it new or something like that is equivalent to the sample standard deviation divided by the mean of the sample. Okay, so for the first step of data were given that essentially The sample standard deviation is 1.55 minutes Divided by the mean, which is three eight minutes. So that gives us a final value for the coefficient of variation Of about 0.4. Well, for the other South data are mean is given us seven points 02 Minutes. While our sample standard deviation is 2.24 minutes. So this is basically has um you of about 2.24 by the seven point there are two, about 0.32. So the importance of essentially the coefficient of variation is basically adjusts the mean, basically the sample standard deviations for the different means. So although it appeared initially that essentially we had greater greater variation and sent to based on just eyeballing the sample standard deviation in actuality, we have a lower coefficient of variation for sent to. So the lower coefficient of variation means for that specific mean, for set two, basically you have lesser variation around the mean, while for basically it's actually greater for someone. So also it's important to be careful not to be misled by essentially the sample standard deviation, basically just by the value of the standard deviation itself unless basically the only case where basically you can directly interpret the sample standard deviation is if you have two different samples with the same mean. So in that case, basically the coefficient forum that isn't really, you don't have to use the coefficient formula since you can directly interpret it from the sample standard deviation right? And the last piece of information were being asked is basically the scariness of the two different sets of data. So for these sets types of data, probably the best way the best way to check for squareness is to use basically dot plots since basically Top Plus can give a good indication, like you have a good indication of the shape of the data. So essentially we can draw dot plots for a set one and set to So the dot plot for set one, the range of values is typically from From the lowest is about zero to the highest, which is about six. So so 123, four and 5. And we're just going to approximate. So 4.21 5.55, 5.13 4.77, 2.34, 3.54, 3.20 4.5 6.1, And 3.79. So, you remember in this case that the average is essentially about 3.88. Yeah, So we can just nearly draw a line here for 3.8. So we can see that approximately the number of values on both sides is relatively equal. So basically this shape of the distribution is nearly symmetric in this case. So there's not really a significance here, nous. And so we're going to do the exact same process for the other set of data in this case for the other set of data being everywhere ranging from Essentially 3.82 To about 11. Maximum of 10.5 or 11. So we can still label or box plot dot plot here. Yeah, Just approximation will be fine in this case. So we have 10.5. About 6.68 5.64 4.08, 6.17 9.91 5.47 9.66 5.90 8.02, 3.82 And 8.35. So we're essentially given that the average in this case is about 7.02. So once again, we can draw a line for 7.02 here approx. So we're we can see that this basically is left. Uh This is less symmetrically distributed, it seems since, but it's still pretty close to the metric, although this has more of a skewed to the right distribution. But it's basically cement it's nearly symmetric basically to about skewed to the right, since the mean seems a little bit higher than it should be compared to the other values. It seems like the mean is being pulled towards a higher value by basically the higher values of the 8910 11 Region.