 Hello and welcome to this session. In this session we will discuss the question which says that Mrs. Samantha is a teacher. She recently gave a test and decided to arrange the scores of 25 students in a stone and leaf plot so that she would see how we are distributed. The scores are 73, 91, 76, 56, 71, 68, 58, 69, 64, 57, 68, 75, 66, 82, 77, 87, 77, 86, 57, 74, 81, 93, 85, 33, 85, 97 and 92 make a stand and leave plot and answer the following questions and the first question is you are earned by more than one student then the second question how many students got at these 85 marks, third one is how many students got less than 57 marks and the fourth one is what conclusion you draw about the shape and spread of the distribution. Now before starting the solution of this question we should know a result that is the stand and leave plot. Now the stand and leave plot constructed by separating into three groups one as a stand and other two separating the data and the very first digit is termed as a leave. Also numbers which we have to arrange in a stand and leave plot so for this number is the stand and five that is the digit at the tens place termed as stand and the digit at units place is termed as a leave and it is written as when we put a line and then we write the leave that is will be written as now here the store will write 4 then we will put a vertical line and then we write the leave that is it means this is the number and secondly this term and leave plot this plot at the distribution of the leaf plot is termed vertically when it gives the shape of the distribution which is the histogram of the distribution and we can tell whether the distribution is symmetrical or skewed. So this result will work out as a key idea so we will have the given question and now we will start with the solution. Now first of all we will form the stand and leave plot so let us arrange the given data from the highest to the lowest value. So we have arranged the given data from the highest to the lowest value now according to the key idea we will form the stand and leave plot and here we will split each number in two parts that is stand so for the stand and leave plot we will separate the numbers in two parts that is the stand and leave and here this stand will be the digit at 10 space we will leave will be the digit units place. Now the first number here is 97 in 97 which is the digit at 10 space is the stand and 7 which is the digit at units place is the leaves 9 then we put a vertical line and then now in the given data the 10 stations vary from 5 to 9 stand vertically from lowest to the highest that is from 5 to 9 then up to 5 we have which is at the 10th space that is 6 then we have 7 so we have written the stand vertically from the lowest to the highest value and then the corresponding leaf is written horizontally from left to right from the lowest to the highest digit. Now from the data we can see that the corresponding leaf with the stand 5 is 6 7 7 so here we will write the corresponding leaves with the stand 5 horizontally from left to right from the lowest to the highest so here first of all we will write 6 then 7 then again 7 and then now the corresponding leaves with the stand 6 and 9 so we will write the corresponding leaves with the stand 6 7 so we have written the corresponding leaves with the stand 7 we will write the corresponding leaves with the stand the corresponding leaves with the stand so we have written the corresponding leaves with the stem 8 and with the stem 9 lot. Now in the first part of the equation it is asked that which course were all by more than one student. Now this time on leaf what you can see that corresponding to the stem 7 the leaf 7 for the stem 5 is repeated twice it means it is repeated twice is repeated twice so this means it's got at least 85 marks we have to find the number of students for their 85 marks or more than that. Now from the part we can see that corresponding to the stem 8 and 7 which means 85 now corresponding to the stem 9 we have the leaves 1 2 3 and 7 which means these marks are greater than 85 that is 91, 92, 93 and 97 which are greater than 85, 91, 92, 93 and 97. The number of students at least 85 marks so these are the 7 students whose course 85, 86, 87, 91, 92, 93 and 97 marks. The third part we have to find that how many students got less than 87 marks now from the plot you can see to the stem 5 the leaf 6 is smaller than 7 corresponding the leaf smaller than the leaf 7 only one student at less than that what conclusion you draw about the shape and spread of the distribution. Now from the key idea we know that describes the spread and shape of distribution when leaf plot is turned vertically then it gives the shape of the histogram of the distribution so now for the shape and spread of the distribution we draw the shape of the histogram which is symmetrical and spread of distribution is wider the shape of a histogram versus symmetrical of the given question and that's all for this session hope you all have enjoyed the session