I wonder if right handed students from the CensusAtSchool NZ 2009 Database are taller than left handed students from the CensusAtSchool NZ 2009 Database. Mr Mounsey

Done by the data viewer.

Dot Plot – Drawn by the data viewer. Box and Whisker – Drawn by the data viewer. SSUMO – on the next few slides.

The shape of the dot plots for both the sample of 30 right handed students from the CensusAtSchool NZ 2009 Database and the sample of 30 left handed students from the CensusAtSchool NZ 2009 Database are both bell shaped but neither is symmetrical. The bell shapes for the graphs are skewed with the students who are shorter than the median being more spread out than the students who are taller than the median. This is especially true for the left handed students. This results in a non-symmetrical bell shape.

The spread for the height of the sample of 30 left handed students from the CensusAtSchool NZ 2009 Database is much greater than the spread for the height of the sample of 30 right handed students from the CensusAtSchool NZ This can be seen by the range of the left handed students ( = 78) being larger than the range for the right handed students ( = 49). This is also seen in by the inter- quartile range of the left handed students ( = 29) being larger than the inter- quartile range for the right handed students ( = 10). Both of these differences are large and can easily be seen on the box and whisker graph.

The only unusual point in the 60 students from the CensusAtSchool NZ 2009 Database is the left handed student with a height of 110cm. This is exceptionally short and is definitely an outlier. This student might have a growth problem or it may be a recording error. If this point is ignored the range of the left handed students from CensusAtSchool NZ 2009 Database is much less ( =53) but is still larger than the range of the right handed students ( = 49).

The middle 50% of the groups of 30 left and right handed students from the CensusAtSchool NZ 2009 Database are centred approximately in the same position. The main difference between the middle 50% of the right handed students and the middle 50% of the left handed students being the spread.

The two boxes on the box and whisker graph overlap. Also the median for the 30 right handed students from the CensusAtSchool NZ 2009 Database is within the box for the 30 left handed students from the CensusAtSchool NZ 2009 Database. The reverse is true as well with the median from the 30 left handed students from the CensusAtSchool NZ 2009 Database being within the box for the 30 right handed students from the CensusAtSchool NZ 2009 Database. Because of this we cannot say one population is taller than the other. The OVS for the two groups is 29 and the DBM is 1. Because the DBM of 1 is not at least a third of the OVS of 29 we cannot say one population is likely to be taller.

The data taken from the CensusAtSchool NZ 2009 Database for the height of left and right handed students shows two things. Firstly that no conclusion can be drawn about the population saying either left or right handed students are taller or are likely to be taller. This is because the medians were within the boxes of the other group and the DBM was not at least a third of the OVS. Secondly that the spread of the data for the left handed students was much larger than the spread of the data for the right handed students in both range and inter-quartile range.

I expected the heights to be the same as which hand someone uses shouldn’t effect how tall they grow. The big difference in the spread is unexpected. It may have come from sampling variability. If another sample was taken the difference in spreads might be less or even the opposite way around. To investigate the difference in spread larger samples should be taken to increase accuracy.

The question was, “I wonder if right handed students from the CensusAtSchool NZ 2009 Database are taller than left handed students from the CensusAtSchool NZ 2009 Database 2009.” Using the 60 student sample the answer to this question is no, they are not taller.