Estimates of a straight line and a curved line

1. I think the older the person is the better they estimate.
2. I also think that if the person estimates within a 10% error of the actual length for one of the lines they will be within 10% of the other line.
3. I think that boys will have a greater spread of data than girls.
4. I think the majority of the girls will b within 10% of the median.

The sentences above may not be true and this is not all I am basing my hypothesis on, but they are a few things that are influencing what my hypotheses are going to be.

2   Hypothesis:

1. If you estimate a curved line accurately you also estimate a straight line accurately.
2. Y10 students have a greater number of pupils within 20% of the median than Y7 students.
3. 50% of all estimates will be within 10% of the actual measurement.
4.  To take all the Quantitative data from Y7 girls and Interpolate the mean.

Collecting data:

                       For my investigation I will make my sample size 50. I will select my 50 by a simple stratified sampling method so everyone has a fair chance of being selected. I will choose these numbers via calculations. I will then do a systematic sample with this data to get the rest of the sample I need.

There’s 102 pupils in Y7 and there’s 111 pupils in Y10so you would do the following calculations.

Y7:    102   x 50 = 24 (2sf)

          214

Y10:  111   x 50 = 26 (2sf)

          214

Then with this data you have to divide the number of pupils needed from the group with the number of pupils in the other group.

Y7:  102 = 4 (1sf)

         24

Y10:  111  = 4 (1sf)

           26

This shows me that I will pick every 4th person from the list of quantitative data from the circus.

Here are the results of the data I collected.

Q1 If you estimate a curved line accurately do you furthermore estimate a straight line accurately? That is what I’m going to investigate into. To do this I will have to construct %error table to decipher whether there is a positive correlation. (error/actual measurement x100). Then I will have to use Spearmen’s Coefficient  of rank correlation.  1 6  d  /n(n –1)

Spearman’s Rank = 1-6  d  /n(n  -1) = 1-6*925/25 (25  -1) = 1-5550/15600=1-0.35576923=0.644230769

Spearman’s rank = 1-6   d  /n(n  -1)=1-6*2701.5/25(25  -1)=1-16209/15600=1-1.039038461

From these two pieces of information I can see that there is a strong positive correlation in boys estimates and no correlation in girls estimates. This tells me that boys, when they estimate either curved or straight line accurately, they also estimate the other accurately aswell. With girls this doesn’t happen. When girls estimate one line accurately, they usually estimate the other line badly.

Q2

When the pupils estimate the curved line, do boys and girls in y10 have a greater number of pupils with 20% of the median than Y7’s. I will have to work the % error for both Y10 and Y7’s.  

I will then have to group the pieces of data to make a cumulative frequency diagram.