TALLY AND FREQUENCY CHART
Now that I have my data I will put them into frequency/tally tables to make it easier to read and it is a useful way of representing and helps view trends within my sampling that I have produced:
Boys Heights
A Pattern I have spotted in this particular Frequency/Tally table is that nearly 75 percent of boys are of the height between 150 to 170 from my sample and this shows me that students in my sample are rather tall and a steady size or above for their age group
Boys Weights
This Tally and Frequency table shows the boy’s weight and the spread of data are large and not as compact as the height whereas the height are rather scattered and vary. This however notifies me that some of the students in my sample and tall for their age but weight are average in relationship to their height.
Girls Heights
This table shows me nearly 50 percent of students are between the height of 150-160 and there are not many student who excel over 180 cm tall which and there are also not many if any student with a height between 130 to 140 cm which shows me that the spread of data is compact which makes it easier to view trends and also it shows that there are not many irregularities in height in the student in my sample that I have taken.
Girls Weight
From this I have found that many girls weigh 40-49 kg and also the girl’s weigh in this particular region or slightly above on most occasions and this shows me that some girls may stop putting weight rapidly after a particular age.
COMPARISONS OF TALLY & FREQUENCY TABLE
I will now compare each of the tables of girls & boys height and then weight and view the differences in trends and if there are and mistakes or bias.
Height Comparison: From the Sample I have taken I have come to find that boys grow rapidly at a later age where as girls grow faster from an earlier age and stop at a particular age also. This is shown since I have found that 2 students are of a height between 130- 139 cm, which shows that my data may be misleading or there is a lapse in growth. Both Girls and Boys have average heights and are fairly balanced and of equal size. Although my Sample shows that boys on some occasion grow to above average height such as over 180 cm whereas in Girls this is rare and unique.
Weight Comparison: Most Boys and Girls weigh in the region of 40- 60 from my sample and I have found that not many girls are over the weight of 60 whereas in Males usually are borderline 60 or above when they come to the age of 16.
This Pie Chart shows the percentage of each year in the School and these help me form my sample and this form of representing data is efficient accurate and eye catching and help form divisions in my data.
Calculations:
Year 7: 281 Divided by 1183 Multiplied by 360
= 86 Degrees
Year 8: 269 Divided by 1183 Multiplied by 360
= 82 Degrees
Year 9: 260 Divided by 1183 Multiplied by 360
= 79 Degrees
Year 10: 219 Divided by 1183 Multiplied by 360
= 67 Degrees
Year 11: 154 Divided by 1183 Multiplied by 360
= 46 Degrees
Total 360 Degrees
MEAN AND MODE OF FREQUENCY DATA
I will now find the Mean, Median and Mode of the Frequency that I have found and this will be quick efficient and reliable and will help me gain evidence on whether boys are taller and weigh more in comparison to girls.
Mean of Girls and Boys Weight
Mean = 1487.3 Divided by 30 = 49.57 rounded off to 50 kg for BOYS
Mean = 1460 divided by 30 = 46.6 rounded off to 47 kg for GIRLS
Mean = Total Frequency Times Midpoint Divided by Total Frequency
MODE OF GIRLS AND BOYS WEIGHT
The arithmetic mean of a group of numbers is found by dividing their sum by the number of members in the group; e.g., the sum of the seven numbers 4, 5, 6, 9, 13, 14, and 19 is 70 so their mean is 70 divided by 7, or 10. Less often used is the geometric mean (for two quantities, the square root of their product; for n quantities, the nth root of their product).
Modal Weight Stem and Leaf Diagram
I have come to find from this stem and leaf diagram shows that the 40 - 49kg weights is the most frequent weight from the sample that I have taken for this particular hypothesis.
Key 3/4 = 34 kg
From this Stem and Leaf Diagram I have also found that the samples of both boys and girls have this there most frequent weight common which although there irregularities or the uncommon heights are less regular which shows that the data is less biased and compact
To find the modal weight I will now look at which frequency seems to have appeared the most often and for the Boys Modal Weight it is:
Modal Group for Boys: 40 ≤w< 50 Modal Weight for Girls: 40 kg
Below is Similar Data but Different Calculation methods to find the Mean, Median and also the Mode as this will help me towards proving my hypothesis also this data will help me find the spread and the average of the data
BOYS: HEIGHT
Mean
1.38 + 1.61 + 1.63 + 1.50 + 1.53 + 1.82 + 1.62 + 1.38 + 1.63 + 1.53 + 1.61 + 1.62 + 1.52 + 1.32 + 1.56 + 1.80 + 1.68 + 1.70 + 1.62 + 1.65 + 1.8 + 1.42 + 1.38 + 1.68 + 1.62 + 1.52 + 1.65 + 1.68 + 1.71 + 1.79
30
= 48.12 Divided by 320 = 1.6
Median: 1.65 m
Range: 1.82 – 1.54 = 0.28 m
BOYS: WEIGHT
Mean: 48.3 kg
Median: 48.3 kg
Range: 64-32 = 32 kg
GIRLS HEIGHT
Mean: 1.55m
Median: 1.55m
Range: 1.75 – 1.39 = 0.36m
GIRLS: WEIGHT
Mean
30 + 36 + 36 +37 + 38 + 40 + 40 + 40 + 41 + 45 + 46 + 47 + 47 + 52 + 52 + 52 +56 + 57 + 59 + 60 + 48 + 36 + 36 + 45 + 51 + 52 + 45 + 55 + 59 + 60
30
= 46.16 which is rounded to 46 kg
Median: 45.5kg
Range: 71 – 30 = 41
COMPARISON OF HEIGHT AND WEIGHT OF BOYS AND GIRLS FROM C.FREQUENCY AND BOX PLOTS
From the Cumulative Frequency Diagram I have come to find that the Median height for boys in the sample that I have taken is larger in comparison to the girl’s median height. Boys Median Height is 165 cm where as Girls Median Height is 155 cm and shows that there is an 10cm difference in the middle figure from both sets of data I have collected although this may on some occasion be accurate due to the fact my sample may not be efficient. As far as the Weights are concerned the range is similar and the range is rather symmetrical also and this may be since my graphs may be irregular.
Scatter Diagram
I will now produce a Scatter Graph which shows the Height vs Weight for all the Boys and girls data that I have collected and I will be able to find whether there is a pure correlation and I will then compare my results and I will see whether my two sets of data are related from my sample:
I will conclude after both graphs
Boys Height vs Weight
[Scatter diagram boy’s height vs weight]
Boys Height vs Weight
[Scatter diagram girl’s height vs weight]
Conclusion of Scatter Graphs
Boys & Girls Height vs. Weight = From the Scatter Graph that I have produced I have come to find that there is a Correlation or a Trend between both variables which are Height and Weight and there is a Fairly Strong Positive Correlation and this shows me that the taller the person the higher the weight although there are always some irregularities which is unique as a symmetrical trend is rather impossible as every human being has various growth period. In addition to this will be the major form of representation in my and I believe this shows the trend clearly and efficiently.
HISTOGRAM AND FREQUENCY POLYGONS
From the data I have collected and formed through my frequency tables and mean averages and many more I will now produce a Frequency Polygon and a Histogram that shows the Boys & Girls Height and Weights From my sample that I have taken a for my assignment. The Frequency Polygon will clearly identify the shape of my variations and both these forms of representing data will help me form a sufficient analysis.
BOYS
Boys Heights
The Following Histogram and Frequency Polygon clearly shows to me that the most common height is between 160 to 169 cm which I believe is average height which in my opinion shows that the hypothesis that I have formulated is correct and is not unbiased. Although both graphs are representing the same data I believe that each graph has its value and help me provide and further in depth analysis and conclude efficiently
[Histogram of boy’s height]
[Frequency Polygon of boy’s height]
Boys Weights
This particular histogram helps me identify the most common weight group which you can clearly view from the histogram and also the frequency polygon which is 50 – 59 kg for boys weight which shows me that is of an average weight for an student studying in the school year of 10 and I have this opinion due to the fact personal experiences although also I have come to find that no one from the sample that I have taken is above the weight does not excel over 79 kg as this polygon clearly expresses and the trend is also lower in frequency from 50- 59 kg onwards.
[Histogram of boy’s weight]
[Frequency Polygon of boy’s weight]
GIRLS
These histograms now give me a clear picture of the data distribution. For the sample there is an even distribution of data. The middle group has the highest frequency which is expected.
Girls Heights
These Representations of Data shows admirably that the average height is 150 to 159 which I believe is slightly above average in my honest opinion for my sample and also I have come to find that the trend is rather varied although the frequency are upward to a certain point and downward from the peak onwards.
[Histogram of girl’s height]
[Frequency Polygon of girl’s height]
Girls Weight
This data shows with great intent that the highest frequency 40 – 49 kg which shows that both boys and girls from the stratified sample that I have taken for this area of my assignment and this hypothesis in particular that they have a lot In common in terms of frequent data sources.
[Histogram of girl’s weight]
[Frequency Polygon of girl’s weight]
CUMULATIVE FREQUENCY DIAGRAMS & WHISKET PLOT
I will now produce cumulative frequency diagram for both girls & boys height and weight and this will help me gain sufficient evidence towards forming my conclusion and I will also find percentiles and will produce box and whisker plots as this will help me view my data and trend efficiently.
Below is a diagram of the Cumulative Frequency & Box-and-Whisker which will help me identify percentiles and trends in my data.
Boys Heights
Cumulative Frequency & Box-and-Whisker Diagram
[Boys cumulative frequency & box-and-whisker of height diagram]
Boys Weight
Cumulative Frequency & Box-and-Whisker Diagram
[Boys cumulative frequency & box-and-whisker of weight diagram]
Form these cumulative frequency & box-and-whisker diagrams i will be able to find the median which will show the middle frequency of my data and also will be able to view the maximum and minimum values for both height and the weight and find the percentiles and the quartiles. For the Height the Median is 162 cm and the interquartile range is 12 cm and the maximum value is 200 cm and minimum value is 130cm. whereas for the weight I have found the Median as 49.5kg which is respectively what I had predictable and is suitably accurate although the range of data for the weight is less and the data in comparison to the height for the boys.
Girls Height
Cumulative Frequency & Box-and-Whisker Diagram
[Girls cumulative frequency & box-and-whisker of Height diagram]
This Cumulative Frequency Diagram I have labeled the Median and Upper and Lower Quartile and through this I will find the spread of data and also I will find the middle number of the data of girls heights that I am investigating and the Median for this graph is 155 cm and the Interquartile range is 160 cm – 149.5 cm = 10.5 cm and this will help toward my final analysis.
Girls Weight
Cumulative Frequency & Box-and-Whisker Diagram
[Girls cumulative frequency & box-and-whisker of weight diagram]
From this I have found the spread on data efficient and on the following page I will compare my results from the cumulative frequency against both boys and girls height and weight and make a suitable conclusion from this representation.
Evaluation of Hypothesis
In my opinion I feel that I successfully completed and analyzed my hypothesis and I have gained a sufficient evidence to back up my theories. I would like to remind you that my main objective for this hypothesis was to find out whether I was correct or incorrect in my thinking that Boys at Mayfield School are taller and weigh more on average than the Girls at the same school. Within this aim I was also aiming to find whether there is a certain trend or relationship between the height and weight of the students that I have chosen to analyse and as I explained earlier due to the large number of students I was not possible to analyse all students so I gained a sufficient sample which I made as unbiased as possible.
Conclusion of Hypothesis
- The Histograms, frequency polygons proved that the results were more accurate and made more sense than that from the random sampling.
- There is a positive correlation between height and weight. In general tall people will weigh more than smaller people.
- In general boys tend to weigh more and be taller then girls.
- By doing stratified sampling, there were a fewer exceptional values caused by different year groups and therefore ages. I was bound to find irregularities within my data.
- The cumulative frequency curves confirm that boys have a more spread out range in weight, with more girls having smaller weights. In height, boys tend to be taller.
- In general the taller a person is, the more they will weigh.
- If I had taken larger samples my hypothesis may become more accurate.