This is used the represent some of the values found from the cumulative frequency graph along with the maximum and minimum values.
- Cumulative frequency graph.
A cumulative frequency graph comes out as a curve that looks like a ‘stretched S’ is called an ogive. The more stretched out the ‘S’ shape is, the more spread out the values are. In a cumulative frequency graph, we mainly look to find 4 pieces of data:
- Lower Quartile - this is the value at 25% of the distribution.
- Median – is the middle value of the distribution (50%).
- Upper Quartile is the value at 75% of the distribution
- Inter – Quartile Range – is the difference in the upper quartile and lower quartile.
This is used the represent some of the values found from the cumulative frequency
graph along with the maximum and minimum values.
This is a way of looking at how spread out the data is. It is basically a discrete data grouped into intervals. The mid – point of each interval is then plotted against the frequency and all these points are joined together with a line.
This is a method of displaying grouped and continuous data. It is similar to a bar chart but it represents continuous data and there are no gaps between bars of a histogram. The area of the bars in a histogram is equal to the size of its frequency.
This is a measure of how spread out the data is. The higher the number, the more spread out the data is. The formula for Standard Deviation is:
Is the measure of the strength of the relationship between two data variables that are linearly related. The correlation coefficient is between -1 and 1.If there’s a positive correlation between the two variables, the correlation coefficient will be positive as well. Every time it gets closer to 1, it means that the data’s are close to the line of best fit and if the C.C. is 1, the data will fit perfectly on the line of best fit.
If the relationship between the data is negative, the correlation coefficient will be also be negative. Every time the C.C. id close to -1, the closer the data are together. If there’s a perfect negative relationship, the C.C. will be -1 where all the data will fit on the line. When the correlation coefficient is 0, this means that there’s no correlation.
The formula for finding Correlation Coefficient is
Plan of action
- Collect data of 30 boys and 30 girls.
- Out of the 30 boys and 30 girls, randomly select 5 boys and 5 girls for first part of pre-test.
- Find the mean of the pre - test height and Handspan for the data.
- Draw pre- test scatter graph of height and handspan and draw a line of best fit.
- Then randomly select 5 more boys and 5 more girls for second part of pre – test.
- Repeat Step 3 & 4.
- Comment on the pre- test finding in relation to hypothesis.
- Move on to the complete data 30 boys and 30 girls and do a grouped data table of the height and handspan of the data.
- Do all data representation and comment on them.
- Comment on findings from investigation in relation to hypothesis.
PRE- TEST
Selecting Data for Pre – Test
To choose which pupil’s data will be used in the pre – test I will use Stratified Sampling. By using this method, all the my data will have an equal chance of being selected as they would be picked at random. To do this, I will divide my data into strata of the classes that my data were collected from.
For the boy’s data:-
- 1 - 12 (12 data’s) were selected from Class 1
- 13 -21 (9 data’s) were selected from Class 2
- 22 - 30 (9 data’s) were selected from Class 3
For the girl’s data:-
- 1 – 15 (15data’s) were selected from Class 1
- 16 – 21 (6 data’s) were selected from Class 2
- 22 – 30 (9 data’s) were selected from Class 3
Calculating Proportion of Data to be taken from each group:
Boys
Girls
To find out the portion of pupils that will be taken from each class group, I will divide the amount of pupils in the class by the total number of pupils altogether which is 30 multiplied by the amount wanted (10). So, for Class 1 of the boy’s data, the proportion of pupils that will be taken from it is:-
I will then apply this pattern to the rest of the data’s
Boys
Girls
After doing this for all the data, I will then randomly selected the proportion of data from each class.
The data’s that will be used for the boy’s pre – test are:
3, 8, 9, 11, 15, 20, 21, 23, 27, 29.
The data’s that will be used for the girl’s pre – test are:
1, 4, 7, 12, 13, 17, 20, 24, 26, 29.
These are the data’s that will be used in the second part of the pre – test. For data’s for the first part of the pre – test, I will randomly select data of 5 boys and 5girls from the already selected above data of 10 boys and 10 girls.
The data’s that will be used for the first pre – test are:
Boys: 3, 8, 20, 23, 27 Girls: 7, 12, 13, 24, 29.
Height and Handspan of 10 boys chosen for Pre- test
Height and Handspan of 10 girls chosen for Pre- test
Result of Pre- test:
From my pre – test, I have found out that there is a positive correlation between the height and handspan of pupils in Y ear 10. This proves that my first hypothesis is correct. I have also noticed that the average of the boy’s height is bigger than the average of the girls’ height which also proves that my second hypothesis is correct. I have also found out that my third hypothesis is correct as the mean of the boys’ handspan is greater than the mean of the girls’.
Overall, from my pre- test I have found out that all my hypothesis are correct.
Mean of Pre test
Boys & Girls Combined Height
169 + 178 + 180 +173 +172 +156 +159 +157 +171 +170
10
= 168.5
Boys & Girls Combined handspan
22 + 24 + 24 + 22 + 24 + 19 +20 + 19 +20 + 19
10
= 21.3
Boys Height:
169 + 178 + 181 + 171 + 166 + 174 + 175 + 180 + 173 + 172
10
= 173.9 cm
Boys Handspan:
22 + 24 + 23 + 20 + 21 + 23 + 23 + 24 + 22 + 24
10
= 22.6 cm
Girls Height:
166 + 161 + 156 + 157 + 159 + 163 + 168 + 171 + 164 + 170
10
= 163.5 cm
Girls Handspan:
17 + 18 + 19 + 19 + 20 +20 + 20 + 20 + 21 + 19
10
= 19.3 cm
Mean
Boys height:
Boys Handspan:
Boys Mean:
Height
(157.5 x 2) + (162.5 x 1) + (167.5 x 10) + (172.5 x 8) + (177.5 x 5) + (182.5 x 4)
30
= 171.7 cm
Handspan:
(19 x 2) + (21 x 15) + (23 x 10) + (25 x 3)
30
=21.9 cm
Girls Height:
Girls Handspan:
Girls Mean:
Height
(142.5 x 1)+ (147.5 x 1)+ (152.5 x 1)+ (157.5 x 9)+ (162.5 x 8)+ (167.5 x 5)+ (172.5 x 5)
30
= 162 cm
Handspan
(17 x 3) + (19 x 16) + (21 x 10) + (23 x1)
30
= 19.2 cm
Cumulative Frequency
Boys Height
Boys Handspan:
Girls Height
Girls Handspan
Boys
Girls
Summary
I have found out that there is a positive correlation between height and handspan of Year 10 pupils. This is shown in my scatter diagram where the line of best fit that is drawn on it shows the positive correlation of the two values. In addition to this, most of the point in my data fit closely to the line of best fit. All this shows that as the height increases, so does the handspan of the pupils which proves that my first Hypothesis is correct.
My second hypothesis which states that “boys will be taller than girls” is also correct. This is proven in the cumulative frequency graph and the box and whisker table for the height of all the data’s. They both show that the middle value (median) for the boys’ height is much greater than that of the girls. The boys’ height median is 171cm which is higher than the girl’s median of 152.3cm. Also, the average of the boys’ height (171.1cm) is bigger than the girls’ mean (162cm). This furthermore undermines that in general, boys are taller girls.
Moreover, I have also found out that my third hypothesis is correct. This is shown cumulative frequency graph and the box and whisker table for the handspan of both boys and girls. Looking at this piece of data, I can clearly see than the median value of the boys’ handspan (21.1 cm) is higher than the median of the girls handspan (19.7 cm) which shows that boys’ have a bigger handspan. Also, the mean of the handspan of both genders also furthermore proves that my hypothesis is correct. The mean of the boys’ handspan is 21.9 cm which greater than the mean of the girls’ handspan which is 19.2cm.
Other information’s that I have found out are that
- The shortest person in a girl
- The tallest person is a boy
- The person with the shortest handspan is a girl
- The person with the biggest handspan is a boy
- Girls have a bigger height range than boys
- Boys have a bigger handspan range than girls
- Most of the girls are155 cm-165 cm tall
- Most of the boys are 165 cm-175 cm tall
Furthermore, I have found out that for both the height, the girls data are more spread out than the boys’ data and the boys’ data is more spread out for handspan than girls. This are shown through Standard Deviation calculation.
The result from the Standard Deviation shows that for height, girls have a higher Standard Deviation which implies that the boys’ data are closer together than the boys. In contrast to this, the result for handspan is a complete reversal with the boys data more spread out as the Standard Deviation for the boys’ handspan is higher than that of the girls.
From the Correlation Coefficient calculations, I have found out that the boys data of both the height and handspan fits closer to the line of best fit than the girls does. This is because the result of the boys’ Correlation Coefficient is 0.506 which is closer to 1 than the girls 0.443.
For these pieces of investigation, I felt that I wasn’t using a large enough sample. I only used a total of 60 Year 10 students. This I feel isn’t a larger enough sample to truly show the relationship between height and handspan of the Year 10 pupils. This is due to the fact that there are over 300 Year 10 pupils in my schools and only using 60 out of 300 isn’t enough. A sample of around 200 would have been better and will give a clearer and a much better picture.
Also, I feel that my method of measuring the data could have been much better. I collected the data primarily (collected it myself). This, even though is a very good method gives more chance of mistakes to be made. Like when measuring the size of the handspan, some people’s hand could have been pulled apart further than other without anyone noticing. This meant that some would have had their maximum handspan recorded whilst others didn’t.
Furthermore, there are other methods of analysing my data that I didn’t do. I did do things like:
- Testing correlation coefficient for significance
