I have completed the collection of data for the hypothesis I am going to work further with this data to find the averages and the Interquartile range of the frequency from the Tests with music and then the tests with out music.
Averages for Tests With or Without music.
Mean
I am now going to get my first average the mean, I will do this by using a mean sum:
With Music
x = ∑ x F
= 74
588
= 7.9459459459459459459459459459459
= 7.94 (2dp) marks in the test
Without Music
= 72
487
= 6.7638888888888888888888888888889
= 6.76 (2dp) marks in the test
Mode
I am now on to the last average mode this simply means the most popular number.
The mode for the Tabloid is 8 Marks in the test.
The mode for the Broadsheet is 6 Marks in the test.
Interquartile Range
I have now completed finding the 2 averages I will now find my Interquartile range. I will do this by finding the lower quartile marks in the test and the upper quartile marks in the test and subtracting the upper quartile from the lower quartile to find my Interquartile range, I will carry this out by using three sums:
With Music
Lower Quartile is 588+1 = 147.25 = 147th (5 marks in the test)
4
Upper quartile is 3 x 588+1 = 441.75 = 442nd (7 marks in the test)
4
The Interquartile range is the difference between the upper quartile and the lower quartile.
IQR = 7-5 = 2 marks in the test
Without Music
Lower quartile is 487+1 = 122 = 122nd (4 marks in the test)
4
Upper quartile is 3 x 487+1 = 366 = 366th (11 marks in the test)
4
The Interquartile range is the difference between the upper quartile and the lower quartile.
IQR = 11-4 = 7 marks in the test
Graphs
I have now recorded all the results and found the averages and the Interquartile range. I will now draw four graphs displaying the frequency, cumulative frequency, and the averages to find out if t he hypothesis proves correct.
These graphs show that my hypothesis is wrong. The first graph shows a high amount of students achieving 5 marks out of 30 this indicates that without the music the students achieved a low mark. However to clarify that my hypothesis are correct the second graph shows a high amount of number of students achieving 7 marks out of 30 indicating that the music helped the students in achieving a better mark, so this show my hypothesis is wrong because students found that music caused them to get better marks.
Graph 3&4
I have studied the first two graphs and am not convinced that my hypothesis are true, I am now going to draw up two Cumulative frequency graphs display the median, upper quartile and the lower quartile of both the With music and the Without music data.
With Music
Without Music
Graph 5
Box Plot
I have completed analysing and comparing the cumulative frequency graphs and am more confident that my hypothesis is correct. But just to confirm I am going to draw the last graph a Box plot graph this graph will display clearer the median, upper quartile and the lower quartile of both the Tabloid and the Broadsheet data.
From this diagram I have noticed that the Broadsheet box is further over on the side of the higher number of letters per word and the Tabloid box is further over on the side of the lower number of letters per word. Now this shows me that the Interquartile range is higher for the Broadsheet than the Tabloid making the hypothesis true. The Broadsheet is a harder newspaper to read.
Interpretation/ Analysis
The first hypothesis. By looking at the tally charts, graphs and box plots for both The Broadsheet and the Tabloid I can clearly see the Interquartile range is larger than that of Broadsheet and the Interquartile range for the Tabloid is lower. The median is also a lot higher in the Broadsheet. The Broadsheet has 10 compared to the 4 of the Tabloid (A difference of 6 letters per word).
The Interquartile range is not as far out though, the Tabloid has I.Q.R of 3 compared to The Broadsheets 5. The upper and lower quartiles are both higher from The Broadsheet. The Tabloid has an upper quartile of 6 when the Broadsheet has 12. The lower quartile is 3 for The Tabloid and 7 for Broadsheet. This suggests that The Broadsheet has more letters on average than Tabloid, but this is only from a small section of the papers.
The tally charts, box plots and graphs for both the Tabloid and the Broadsheet from the report shows that the Broadsheet has a larger Interquartile range than Tabloid. The upper quartile range is 12 and the lower quartile is 7 giving the broadsheet an Interquartile range of 5 whereas Tabloid has an upper of 6 and a lower of 3 giving it an Interquartile range of 3. The upper quartile is a lot higher for Broadsheet which overall means it has larger words than Tabloid for this article.
The tally chart, box plots and graphs for both Broadsheet and the Tabloid from the reports shows that the median is higher for Broadsheet it is 10 compared to the 4 of the Tabloid. The Broadsheet has a larger Interquartile range than Tabloid. The upper quartile is 12 and the lower is 7 which giving the Broadsheet a 5 for the Interquartile range. The Tabloid has an upper of 6 and a lower of 3 which gives the Tabloid a 3 for the Interquartile range. The Broadsheet has a higher median and a higher upper quartile than Tabloid. This suggests that the Broadsheet has a higher letter count than the Tabloid.
The tally charts, graphs and box plots show all 3 reports grouped together. This gives an overall view of the paper. The box plots show that the papers have a different median, upper and lower quartiles so therefore has a different Interquartile range. Proving my hypothesis true.
The cumulative frequency diagram shows Broadsheet to have a greater frequency of letters per word. Tabloid has more medium to lower size words than Broadsheet. The graph shows wide spread of data in the Broadsheet.
The Broadsheet has a larger mean than Tabloid 8.9 compared to 4.6 this is a quite big difference but maybe could have been achieved by chance.
Hypothesis Two
The second hypothesis was the longer the headline the longer the article. I gathered 9 articles from the Broadsheet and 9 from the tabloid I then recorded all the letters in the headline and the words in an article for all 18 articles and I ended up with two charts with the tabloid and broadsheet results I noticed something happening with the data and decide to draw up two scatter graphs to see if I had weak, strong or no correlation and as I thought I found for both the tabloid and broadsheet strong correlation, but there were a few in the broadsheet and tabloid anomalies which worried me and made me think there could be In a wider range of data more and proving my hypothesis wrong. But for this amount of data to find if the longer the headline the longer the article, my hypothesis was correct.
Hypothesis three
For the second hypothesis my task was to find out if in 15 pages of broadsheet there are more adverts than in 30 pages of a tabloid. To find my results I counted all adverts on 15 pages of a broadsheet and also for 30pages of a broadsheet and recoded the results on a table, then I found the total area of a page in a broadsheet newspaper and also for tabloid and then found the all the adverts area in a broadsheet and tabloid. To see if my hypothesis was true I found the proportion of all adverts in all 15 pages of a broadsheet and 30 pages of a tabloid and divided by the total area of all pages which gave me to percentages which I recoded and compared on my pie chart. This proved my hypothesis to be correct.
Conclusion/Evaluation
My prediction is correct for the first hypothesis. In the conclusion the results suggest that the broadsheet has more letters per word on average than tabloid, but this does not mean that this is conclusive. There is only a small sample that has been taken. If there was more time larger, more wider investigations could have been taken. I could have investigated other newspapers. I could also of have investigated on the size of photographs or pictures that were in the papers, to see if there was a correlation between the size and number of pictures to the size of the words. A factor was there not being enough time to complete all three hypothesis. Word size might not mean that the paper is more profound or easier to read, this assumption I made may be false and invalidate the investigation, this means my conclusion for the first hypothesis is not definite and I can not take it far.
My prediction was also correct for the second hypothesis. In the conclusion my results showed me that both the broadsheet and the tabloid had positive correlation indicating to me that my the longer the headline the longer the article. I again don’t positively think this is conclusive because the wasn’t enough data collected if more newspaper were use and more data was gathered then I would get a more accurate final result to conclude to my hypothesis to see if I was right or wrong.
For hypothesis three if I had more time I would of made a wider investigation to see if in 15 pages of a broadsheet there are more adverts than in 30 pages of a broadsheet because my hypothesis could be proved wrong. In different tabloid newspapers and different broadsheet there might be different results so this hypothesis is not entirely accurate.
Tyrone Thomas Burns 11MC 08/05/2007 Page of
