Read All About It
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Introduction
John Saunders (R)
Maths coursework: Read all about it
In this investigation, I will be comparing magazines and newspapers. I will compare things such as the length of words in articles and the number of articles in them, as you will see in my hypotheses.
I will use several different magazines and papers to try and make my final results a little more accurate, and so I can extend on what I can compare, again as you will se in my hypotheses.
Papers/magazines I will be using:
Newspaper  Details  Magazine  Details 
Daily Mirror  For Thursday June 27th 2002  Shoot Monthly  For July 2002 
Daily Express  For Friday June 21st 2002  What’s on TV  For 612 July 2002 
The TV mag*  (Supplement from ‘The Sun’ – for 6th July 2002)  
F1 Racing  For July 2002 
*A supplement
Calculations:
Throughout this piece, I will be using some calculations quite a lot, to work out certain things which are vital in working out whether my hypotheses are correct. These include:
 X = ∑fX ÷∑f
Mean = The total of (frequency x no. of words) ÷ The total number of words
This equation is for working out the mean average of a frequency distribution. It isn’t possible to work out the mean using the normal method in a frequency distribution, because the norm doesn’t account for all the measures for all the numbers (in other words, no matter what differences there are in the number of letters in each word, the total of all the words taken into account will always equal the number the distributed numbers add up to).
For example, in hypothesis one, no matter how the tally ends up like, whether there are 100 twelve letter words or 100 one letter words, the total number of words used in the normal mean would always have to be taken as 100, because that’s what the distribution would always add up to.
2) X = ∑
Middle
60.5
5
10
14
12
60
72.5
6
5
4
4.5
27
77
7
13
10
11.5
80.5
88.5
8
8
4
6
48
94.5
9
1
3
2
18
96.5
10
3
0
1.5
15
98
11
1
0
0.5
5.5
98.5
12

2
1
12
99.5
13

1
0.5
6.5
100
∑fX
448.5
Mean = ∑fX ÷∑f
(Mean = The total of fX ÷ The total number of words)
Mean = 448.5 ÷ 100
Mean = 4.485 letters per word
Standard Deviation of the results:
No. of letters (X)  Average frequency (f)  X  X  (X – X)²  f(X – X)²  
1  5  3.485  12.145225  60.726125  
2  15.5  2.485  6.175225  95.7159875  
3  20  1.485  2.205225  44.1045  
4  20  0.485  0.235225  4.7045  
5  12  0.515  0.265225  3.1827  
6  4.5  1.515  2.295225  10.3285125  
7  11.5  2.515  6.325225  72.7400875  
8  6  3.515  12.355225  74.13135  
9  2  4.515  20.385225  40.77045  
10  1.5  5.515  30.415225  45.6228375  
11  0.5  6.515  42.445225  21.2226125  
12  1  7.515  56.475225  56.475225  
13  0.5  8.515  72.505225  36.2526125  
∑f  100  ∑f(X – X)²  565.9775 
S.D. = √ ( ∑f(X – X)² ÷ ∑f )
S.D. = √ 565.9775 ÷ 100
S.D. = √ 5.659775
S.D. = 2.379028163
This means that 67% of all the results are within 2.37 (approx.) letters of the mean, which was 4.485
This shows that the standard deviations of both averages are very similar, as the differences between them is only 0.05 (2.37 – 2.32). This also reflects the small difference between the averages:
4.53 – 4.485 = 0.045 letters per word
As you can see, I proved my hypothesis was correct, although I was expecting a much larger difference between the two mean averages. On the next few pages there are several graphs to represent this data in many different ways, mainly to compare the two.
This also shows that the mean AND standard deviation between magazines and newspapers have a very close relationship with each other. This means that the results were almost identical.
Graph 1.1 (page 10):
This graph is a cumulative frequency graph. As you can see, the graph seems to be correct, because it is in the ‘S’ shape that all cumulative frequency graphs end up being in. The lines are in very similar positions, which reflect on the tiny difference between the averages of the difference in letters per word. The red line that represents magazines, shows there are slightly more words that are between 36 letters and 810 letters long. After these (7 and 1112 letters), there are more letters per word, because the lines even out again.
Apart from this, the blue line (representing newspapers), and the red line are virtually identical, meaning there are the same numbers of letters per word up to that point on the graph.
Graph 1.2 (page 11):
This is a line graph representing each individual result, and not the cumulative frequency, and again, the blue line represents newspapers and the red line represents magazines. Unlike the cumulative frequency graph, these results are fairly different in most letter categories, but never the less follow the same trend.
The only two major exceptions to the trend are in the fiveletter category  where in the newspapers there are more words than in the fourletter category; whereas in magazines there are fewer words than in the fourletter category  and in the sevenletter category  where in newspapers there are more words than in the six letter category; whereas in magazines there are less words in the sixletter category.
The green line represents the general trend of both graphs. It shows that the general trend is positively skewed, because the mean is greater than the median and the mode – which is telling us that as you go further along the ‘x’ axis, there is a less and less number being represented on the ‘y’ axis. This is why the mean is higher – because the mean is affected by smaller amounts of possible anomalous results, whereas the median and mode aren’t, and because the anomalous results appear to be the higher letter frequencies, then this will make the mean a greater number.
Survey results:
No. who thought answer was newspapers  % who thought answer was newspapers  No. who thought answer was magazines  % who thought answer was magazines  No response  
Year 7  10  63%  6  37%  0 
Year 8  12  86%  2  14%  0 
Year 9  10  77%  3  23%  0 
OVERALL TOTAL (of 43)  32  74%  11  26%  0 
*Percentages to nearest whole number
This shows that the year seven’s had the best idea of what the answer turned out to be, because the answers they gave were the most similar in number (with a range of four), which reflects upon the similarity of the number of letters per word on average.
This also shows that the whole of KS3 would be correct, as the majority (74%) thought that newspapers would have the longer words on average.
Hypothesis two:
(There will be more articles in newspapers than in magazines)
For this, I am going to use a similar method to the one I used in hypothesis one, except I am going to use the first 40 pages from the magazines and newspapers, and I am going to use class intervals of five pages to make my results table easier to understand.
Here are the newspapers and magazines I will be using (details of them can be found on page one):
Newspaper 1: Daily Express Magazine 1: F1 Magazine
Newspaper 2: Daily Mirror Magazine 2: Shoot Monthly
From these, I will count the number of articles on each page, and input the data into the relevant box, as a tally at first, but then as overall totals later.
There are only two major problems I see with this. The first one is that if an article begins on one page in one interval and finishing on another page in a different interval. To solve this, I am simply going to say that any article will be classed to be on the page it begins on. For example, if there were a double page spread on pages 20 and 21, then it would go in the 1620 category because the article starts on page 20.
The second problem is that if the magazines start on page 4 or 5, due to the contents or an introduction etc. at the beginning. To solve this, I am going to simply put a ‘0’ in the 15 if this occurs, because if I didn’t, it would make the graphs a lot harder to compare and the tables more confusing.
Tally of no. of articles in ‘x’ pages  
Pages  Newspaper 1  Total  Newspaper 2  Total  Magazine 1  Total  Magazine 2  Total 
15  //// ///  8  ////  4  0  /  1  
610  //// //// /  11  //// ////  10  /  1  ///  3 
1115  //// ////  10  //// /  6  0  ///  3  
1620  ///  3  //// ////  10  ///  3  ///  3 
2125  ////  5  ///  3  //// ////  10  ////  4 
2630  //// ////  9  //// ///  8  //  2  //  2 
3135  ////  5  ////  4  /  1  /  1 
3640  ////  5  //  2  /  1  //  2 
Σf  56  47  18  19 
As you can see, it doesn’t take too much common sense to realise that hypothesis two is again correct. For the sake of preciseness though, I will work out the mean averages:
Mean average for newspapers:
Page no’s.  Value of X  Frequency for newspaper one  Frequency for newspaper two  Average frequency (f)  
15  3  8  4  6  
610  8  11  10  11.5  
1115  13  10  6  8  
1620  18  3  10  6.5  
2125  23  5  3  4  
2630  28  9  8  8.5  
3135  33  5  4  4.5  
3640  38  5  2  3.5  
∑f  52.5 
X = ∑X ÷ N
(Mean = The total of the single frequencies ÷ the number of frequencies)
Mean = 52.5 ÷ 8
Mean = 6.56 articles per interval, which means…6.56 ÷ 5 = 1.31 articles per page
Mean average for magazines:
Page no’s.  Value of X  Frequency for newspaper one  Frequency for newspaper two  Average frequency (f)  
15  3  0  1  0.5  
610  8  1  3  2  
1115  13  0  3  1.5  
1620  18  3  3  3  
2125  23  10  4  7  
2630  28  2  2  2  
3135  33  1  1  1  
3640  38  1  2  1.5  
∑f  18.5 
X = ∑X ÷ N
(Mean = The total of the single frequencies ÷ the number of frequencies
Mean = 18.5 ÷ 8
Mean = 2.31 articles per interval, which means…2.31 ÷ 5 = 0.46 articles per page
The difference between the no. of articles per page: 1.31 – 0.46 = 0.85
Although this looks as if it was pretty fair, I think that part of the problem with the magazines is that some articles were several pages long, and there were a lot more pictures in them. Never the less, the point of the hypothesis was to find the number of articles despite these kind of problems, so this hypothesis must be correct.
Graph 2.1 (page 16):
This is a graph to show the correlation between the two variables. Unlike in the graphs on pages 6 and 7, these points aren’t joined up together. This is because we are looking to see how well the lines would fit together supposing we put them on a line of best fit. You can see a blue line on this as well – this is a regression line, which is simply a line of best fit.
There is a point on the graph at (6.56, 2.31) that this line goes through, this is the coordinate that shows the average frequencies for both the ‘x’ and ‘y’ axis (i.e. 6.36 and 2.31 are the average frequencies of articles in newspapers and magazines per page). The working out for this is on page 15. This has given me some idea of where to place my line of best fit to make it correct. I don’t think it shows the line of best fit too well, but only because the circled anomalous result made the average coordinates larger than they would have been supposing it wasn’t there.
Coefficient of rank correlation for newspapers and magazine (for basic details on correlation, see page 1):
Page no’s.  Frequency for newspapers (average frequency)  Frequency for magazines (average frequency)  Rank for newspapers  Rank for magazines  Difference (d)  d²  
15  6  0.5  5  8  3  9  
610  11.5  2  1  3.5  2.5  6.25  
1115  8  1.5  3  5.5  2.5  6.25  
1620  6.5  3  4  2  2  4  
2125  4  7  7  1  6  36  
2630  8.5  2  2  3.5  1.5  2.25  
3135  4.5  1  6  7  1  1  
3640  3.5  1.5  8  5.5  2.5  6.25  
∑d²  71 
R = 1  __6∑d²__
n(n²  1)
R = 1  __6 x 71__ = 1 – (426 ÷ 504) = 1 – 0.84 = 0.16
8(64 – 1)
This shows that the correlation between the number of magazine and newspaper articles per page is very low. This is what I was expecting to happen on the graph, as the results seemed to be scattered in no particular order. Especially with taking the anomalous result (circled on graph) into account, the results of this formula seem to have come out right.
Regression line equation:
Page no’s.  Frequency for newspapers (average frequency)  Frequency for magazines (average frequency)  
15  6  0.5  
610  11.5  2  
1115  8  1.5  
1620  6.5  3  
2125  4  7  
2630  8.5  2  
3135  4.5  1  
3640  3.5  1.5  
∑f  52.5  18.5 
Conclusion
Despite these problems, I am satisfied that the results I got from the data were accurate, even to say that some results didn’t match what I thought the results should have been prior to doing the tests.
This student written piece of work is one of many that can be found in our GCSE Comparing length of words in newspapers section.
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