 Hello and welcome to the session. In this session we will discuss how to represent a data in a dot plot and box plot display. Now a dot plot is a graph that shows frequency of data along a number line. Now let us see the steps for making a dot plot. First we collect the data and once the data is collected it is then time to make a dot plot. In the first step we draw a number line. For this we determine the scale to be used. It means take equal distance between the consecutive numbers on the number line. For example we can take numbers at a distance of 5 like 5, 10, 15, 20 and so on or at a distance of 10 like 10, 20, 30, 40 and so on. It all depends on the numbers in the data. In the second step we label the number line like if we are representing height in inches, length in centimeters, temperature in degrees etc. We write it along the number line. We also give title to the graph like whose data is being represented. Then in the next step list the data when place a dot over the correct number for each of the observation collected. If a number is repeated then place a dot above the other. Now suppose if in the given data we have a number 50 that is we have observation 50. Then we will place a dot here and if the number 60 is coming twice in the given data then we will place a dot above the other. And now let us discuss an example. Here the wildlife department surveyed 44 female bears to measure their lengths in inches and the family observations were recorded. Now let us make its dot plot. First of all we make a number line. Now here we see that values are from 36 to 70 so we take a scale of 5 or 10 as convenience. Now here let us write the values starting from 30 and we will take scale of 5. So here the values will be 30, then 35, 40, 45, 50, 55, 60, 65 and 70. Since the observations are the lengths in inches thus label this number line as length in inches. And now we put a dot for each observation given in this data. And if the observation is repeated say 58 is repeated 5 times then we place 5 dots one above the other at point 58 on the number line. Now let us put the dots. Now here 36 is coming once so we will put one dot here, then 44 is coming once so we will put a dot here, then 46 is coming twice so we will put a dot over the other. That is we will put two dots here one above the other. Similarly we will put the dots for other observations also. So here we have put the dots for all of these observations. And now we give a suitable title to the plot and here we are measuring length of female bears. So we give title female bears and here number of observations that is n is equal to 44 at vertical dot bars in the graph. This is the required dot plot for the given data. Now in level 1 we have already discussed how to construct a box and whisker plot. Now we construct the box plot for the above data with outliers. For this we first point median upper quartile, lower quartile and interquartile range. Now here number of observations or we can say number of terms n is equal to 44 which is even. Now median is the middle value and it will be equal to 22nd term plus 23rd term, 0.2 which is equal to 59 plus 59 whole upon 2 and this is equal to 118 by 2 which is equal to 59. Now let us denote median by 2. Now 22 items or 22 terms lie below median value and 22 lie above the median value. Now let us find the lower quartile q1 which is equal to middle value of lower 22 terms and this is equal to 11th term 12th term whole upon 2 and this is equal to 56 plus 57 whole upon 2 which is equal to 113 upon 2 which is equal to 56.5 and now let us find upper quartile q3 which is equal to middle value of upper 22 terms 61 plus 62 whole upon 2 which is equal to 123 upon 2 which is equal to 61.5. Now let us find interquartile range which is equal to upper quartile minus lower quartile and this is equal to 61.5 minus 56.5 which is equal to 5 and now we will check for the outliers and we see the range q1 minus 1.5 into interquartile range q3 plus 1.5 into interquartile range. Now let us find this value and it will be now q1 is 56.5 minus 1.5 into interquartile range which is 5 is equal to 56.5 minus 7.5 which is equal to 49. Now let us find this value now it will be q3 now q3 is upper quartile which is 61.5 plus 1.5 into 5 is equal to 61.5 plus 7.5 which is equal to 69. Now the values in the given data line below 49 and above 69 are outliers so 36, 44, 46, 48 and 70 are outliers. So we draw the box with whisker here the box starts from the lower quartile q1 to upper quartile q3 and this blue line that is this blue vertical line represents median and we do not cover outliers in a discuss. So in this session we have discussed how to represent a data in a dot plot and box plot display and this completes our session hope you all have enjoyed the session.