The table shows the year groups of some students who use the canteen. Mr Ford wants to survey 50 of these students stratified by year group. How many more year 9 students than year 8 students should be in the survey?

7 more year 9 students than year 8 students should be surveyed, If Mr.Ford wants to survey 50 of these students stratified by year group.

Step-by-step explanation:

The given is,

                    Year                        Students

                       7                                 80

                       8                                 110

                       9                                 160

                    Total                              350

           Mr.Ford wants to survey 50 of these students stratified by year group.

Step:1

           Formula to find the ratio of number of grouped students to total students,

                                         =

                                         = 0.1428

Step:2

          Formula for Number of students surveyed from year wise,

          For year 7 students,

                                         = (Ratio) × (Students from year 7)

                                         = 0.1428 × 80

                                         = 11.424

                                        ≅ 11               (∵ For students we convert into whole number)

         For year 8 students,

                                         = (Ratio) × (Students from year 8 )

                                         = 0.1428 × 110

                                         = 15.708

                                        ≅ 16               (∵ For students we convert into whole number)

          For year 8 students,

                                         = (Ratio) × (Students from year 9 )

                                         = 0.1428 × 160

                                         = 22.8

                                        ≅ 23             (∵ For students we convert into whole number)

Step:3

          To find How many more year 9 students than year 8 students should be in the survey

                                        = ( Students from year 8 for group) -

                                                                     ( Students from year 8 for group)

                                        = 23 - 16

                                        = 7 students

Result:

          7 more year 9 students than year 8 students should be surveyed, If Mr.Ford wants to survey 50 of these students stratified by year group.