Data Handling Coursework

        To find out my 60 samples I am going to use random sampling, I will do this using my calculator to pick out random numbers. To do this I will put the number of people in a year and then press the ‘Ran #’ key, this will pick a random number. I would then look on the data sheet and pick the height and weight of the number chosen. Some problems might occur when randomly sampling as if I was to get 15 year 7 boys and the random number came up twice, the number was erroneous or if I got a number, which was a girl, I would have to do the number again and leave out the wrong number.

Samples

Year 7

Year 11

  Hypothesis 1

        I am going to use a scatter diagram to see the relationship between height and weight. I will try to find out if taller you are then heavier you weigh.

        My hypothesis was right. By using my scatter diagram I can see the tallest boy, which is in year 11, weighs the heaviest of all the year 7 and 11 pupils. The year 11 boy is 1.86m in height and weighs 80kg. Also if taller you are the more you weigh then smaller you are the less you weight and I can see this on my scatter graph as the year 7 girl is 1.41m in height and weighs 39kg.  

Hypothesis 2

        I am going to use a stem and leaf diagram to organise the data and then using this I am going to use a box plot to try and find out if year 7 boys are lighter than year 11 girls.

Stem and leaf

Year 7 boys weights

LQ =        15 + 1                

4

 =  4th

 =  40

UQ  = 3(15 + 1)

                 4

        =  12th

        =  50

IQR = UQ – LQ

        = 50 – 40

        =  10

Median = 15 + 1

                 2

   =  8th

             =  43

Year 11 girls weights

LQ =        15 + 1                

4

 =  4th

 =  35

UQ  = 3(15 + 1)

                 4

        =  12th

        =  50

IQR = UQ – LQ

        = 50 – 35

        =  15

Median = 15 + 1

                 2

   =  8th

             =  42

Now using these calculations I am going to use a box plot to try and see if my 2nd hypothesis was right or not.

        My hypothesis was wrong. In fact year 7 boys overall, weigh more than year 11 girls. I have found this out by using my box plot. The year 11 girls LQ is less than the year 7 boys lowest weight value. The year 7 boys highest value is a lot more than the year 11 girl’s highest value and the UQ of both years and gender is exactly the same. Year 7 boy’s median is a little more than the year 11 girl’s median. Year 11 girls have a larger spread than year 7 boys. The year 7 boys IQR is more than the year 11 girls IQR.

Hypothesis 3

I am going to use a stem and leaf diagram to organise the data and then using this I am going to use a box plot to try and find out if the spread of year 7 boys heights are larger than the spread of year 7 girls heights.

Stem and leaf

I am going to change the metres into centimetres so it is easy to work out the LQ, UQ, box plots, etc.

Year 7 boys heights

LQ =        15 + 1                

4

 =  4th

 =  149

UQ  = 3(15 + 1)

                 4

        =  12th

        =  161

IQR = UQ – LQ

        = 101 – 149

        =  12

Median = 15 + 1

                 2

   =  8th

             =  155

Year 7 girls heights

LQ =        15 + 1                

4

 =  4th

 =  142

UQ  = 3(15 + 1)

                 4

        =  12th

        =  162

IQR = UQ – LQ

        = 101 – 149

        =  20

Median = 15 + 1

                 2

   =  8th

             =  156

Now using these calculations I am going to use a box plot to try and see if my 3rd hypothesis was right or not.

My hypothesis was wrong. In fact the spread of year 7 boys heights was smaller than the spread of year 7 girls heights. I have found this out by using my box plot. The year 7 girls LQ is the same as the year 7 boys lowest height value. The year 7 boys highest value is a lot more than the year 11 girl’s highest value and the UQ of year 7 girls is a little more than the year 7 boys UQ. Year 7 boy’s median is a little less than the year 7 girl’s median. The year 7 boys IQR is less than the year 7 girls IQR.

My project could have been improved by using data on a real high school in this area. I could’ve used more samples to get more results. I could have picked my samples different ways such as picking it out of a hat.