I have chosen to gather my information by using stratified sampling. I have chosen this process as I feel it is the easiest and most efficient method. I also want to take an equal percentage of boys and girls from my samples so that it is fair.
Year 7 sampling
There are 182 pupils in year 7 I want a sample of 20%.
20 x 182 = 36
100
Boys
74 x 36 = 15
182
I told my calculator that my data values went up to 182 the used the “Ran#” button on my calculator to randomly choose the 15 boys.
Girls
108 x 36 = 21
182
Year 10 Sampling
There are 180 pupils in year 10 and I want a sample of 20%
20 x 180 = 36
100
Boys
87 x 36 = 17
180
Girls
93 x 36 = 19
180
Finding the mean, median and mode
Year 7
Mean
46.5 = 1.291666667
36
mean = 1.29 m
Mode
The modal class is : 1.40 L 1.60
Median
The median is found in the class interval 1.40 L 1.60
Range
1.60 – 0.50 = 1.10
Year 10
Mean
55.2 = 1.53
36
mean = 1.53 m
Mode
The modal class is : 1.20 L 1.40
Median
The median is found in the class interval 1.40 L 1.60
Range
4.80 – 0.95 = 3.85
The mean will tell us the overall average of people’s estimates. The median is to find the middle value, the mode will tell us the value that has appeared the most in the data, and the range will tell us the difference between the highest and the lowest data values. Standard deviation will tell us the variation in the whole data set.
Cumulative frequency tables
From drawing these tables I can now draw up cumulative frequency graphs to find out the lower quartile range, upper quartile range and the inter quartile range.
Year 7
Upper quartile range:
3 of 36 = 27
4
U.Q.R. = 1.53
Lower quartile range:
1 of 36 = 9
4
L.Q.R. = 1.28
Inter quartile range:
U.Q.R – L.Q.R = I.Q.R
I.Q.R. = 1.53 – 1.28 = 0.25
Median
27 – 9 = 18
median = 1.54
Year 10
Upper quartile range:
3 of 36 = 27
4
U.Q.R. = 1.60
Lower quartile range:
1 of 36 = 9
4
L.Q.R.= 1.25
Inter quartile range:
U.Q.R – L.Q.R = I.Q.R
1.60 – 1.25 = 0.35
Median
27 – 9 = 18
median = 1.41
Conclusion
From processing the data I see that the year 7 with a mean of 1.29m are better at estimating length than the year 10’s with a mean of 1.53m are. Although the year 10’s mean was only 0.17m away from the actual length of the stick, this could indicate that if the data was processed again the year 10’s might be better at estimating length.
The year 10’s had a higher standard deviation than the year 7’s this indicates that some of the year 10’s data values were either very high or very low. The range confirms this, as there is a difference of 3.85 between the highest and lowest values. This tells us that this group could have been completely changed by 1 person either estimating too high or too low.
From my tables I can see that most year 7’s estimations were in the 1.40 L 1.60 group and most of the year 10’s estimations were n the 1.20 L 1.40. This tells us that the year 10’s estimated more values in the right group but the very high vales distorted the overall mean.
I conclude that the year 7’s in this case were better at estimating length than the year 10’s were. This however could change if the sampling were to be done again.
Evaluation
I think that I produced a valid and suitable investigation. I made sure that all my sampling was done fairly and randomly. I also took into consideration my aim throughout my experiment so that I could perform it suitably.
I feel there are things that could have been done to improve my investigation. I think that when gathering the information pupils could have been asked to do this separately as they might have copied what someone else had put. From the data values u can see that some people just put down the height that they were told a door was. This could have maybe could have been stopped If they were also told they weren’t allowed to put down the height of a door as their answer. This is what I would do if the data was collected and processed all over again.
