 Hello and welcome to the session. In this session, we will discuss a question with phase that constructs the wax and viscous plot for the given data showing the speed in miles per hour of vehicles on a highway and the speeds are given to us as 50, 100, 70, 80, 90, 25, 90, 100, 90, 70, 50, 50, 90, 100, 50 and 90 miles per hour then from the box and viscous plot what do you interpret? Now let us start with the solution of the given question. Now here we have to construct a box and viscous plot for this given data. So here in the first step we will arrange the given data from the least to the greatest. So arranging the given data we get 25, 50, 50, 50, 50, 70, 70, 80, 90, 90, 90 then again 90, 90, 100, 100 and 100. Now here the number of items in this given data that is n is 16 which is even. Now here the number of terms is even so median let it be q is equal to the mean of two middle values that is the mean of eighth and ninth term which is equal to 18 plus 90 whole upon two which is equal to 170 upon two which is equal to 85. So median will lie in between 80 and 90. Now we know that median of lower half of data set that is the values below median value is lower time and median data set that is the values above the median value is upper quartile. So here the lower quartile let it be q1 is equal to now here you can see in the lower half of data set we have eight items the median of these values will be equal to the mean of middle values. So lower quartile q1 is equal to 50 plus 50 whole upon two which is equal to 100 upon two which is equal to 50 and similar let it be q2 is equal to the mean these two values which is equal to 90 plus 90 whole upon two which is equal to 180 upon two which is equal to 90. Also you can see that the least value of this data set is 25 and the greatest value of this data set is 100. Now for constructing a box and whisker plot for the given data we will plot these five values on the number line so here we have drawn a number line let us plot the extreme values that is 25 the median q which is equal to 85 then the lower quartile which is q1 that is equal to 50 and then the upper quartile which is q2 that is equal to 90 then we will draw a box starting from the lower quartile which is 50 quartile which is 90 so here we have drawn a box in which this vertical edge shows the lower quartile q1 this vertical edge shows the upper quartile q2 and this vertical line inside this box shows the median q at the minimum maximum values here at each quartile to these extreme data points the whisker plot for the given data now from this box and whisker plot we can interpret that the data is widely spread between the lower quartile q1 the median q of the data that is in this portion and q of the given question and that's all for this session hope you all have enjoyed the session