‘Broadsheets are harder to read than tabloids’ - Maths Investigation

The rules I came up with are:

* Anything with a capital letter and a full stop is a sentence. E.g. Oh Dear.

* Numbers don't count unless written. E.g. twelve

* Quotes count.

* Names count, the forename and the surname

* Hyphenated words count as 2 words. E.g. water-shed. The exception to this rule is if a word is hyphenated because it would not fit on the end of a line; for example if 'exagger-' appeared on one line, followed on the next by 'ated', it would be counted as only one word.

* Abbreviations count as words.

* Words like NATO or US count as words.

After counting all of the sentences, I realized (because of article length) that I had three more sentences in the broadsheet than in the tabloid; I think this will have little effect on my results but this may be an interesting point to raise later.

Analysis

NOTE: To prevent meaningless figures, all values will be rounded to the nearest whole number where appropriate.

Now that I have collected my data I must begin to analyze it, this will be the most important part of my investigation.

Cumulative Frequency

To begin with I will make a cumulative frequency diagram for both the broadsheet and the tabloid. These can be seen on the graph paper.

This graph shows some important details. It shows the upper and lower quartiles, and the interquartile range. It also shows me the median, which is one of the three averages I will be finding in order to compare my data.

Type Of Newspaper

Upper Quartile

Lower Quartile

Interquartile Range

Median

Tabloid

25

1

4

7

Broadsheet

28

3

5

20

As you can see from these results that the spread of the broadsheet is bigger and that the median is higher, but this gap is very small and the results are very similar But to say that these results are relevant is wrong especially as the results have no link, so I will standardize the interquartile range to get rid of this problem. I will get the Standardized interquartile range by using this formula

Interquartile Range

Median

Standardized Interquartile Range (to 2 D.P.)

Tabloid

4

7

0.82

Broadsheet

5

20

0.75

I am also going to draw box plots to make this information easier to analyze.

After seeing these I have realized that so far it seems that the broadsheet has a higher median and a larger spread of data, but with the data being very similar I am starting to believe that the hypothesis may not be as accurate as I thought.

Histogram

In drawing a histogram I will be able to find the mode and see the spread of data easily. Finding the mode enables me to compare which newspaper has the highest most common value.

After drawing the histograms I found that the broadsheet had a higher mode meaning, that the most common value in the broadsheet is higher than that of the tabloid.

The histogram has a frequency polygon showing the spread of data. From this I can see that the broadsheet, is higher further along the graph, where as the tabloid hoes up quick and then down slow.

The Mean

The third and final average shows me an average while taking every piece of data into account. From the mean I can find the standard deviation, which shows my spread of data. I will get the mean by using this formula

I will get the standard deviation by using this formula

Mean

Standard Deviation

Tabloid

7.81

9.37

Broadsheet

20.40

8.81

As you can see from this data, the mean (taken from ungrouped data) may be higher, but the spread of data is the same. Showing that, they both have the same range from their mean. This shows they are very similar and that the tabloid is generally lower than the rest.

Maybe the hypothesis isn't so correct.

Now I am going to compare these to the grouped data. My results are in this table.

Mean

Standard Deviation

Tabloid

7.12

9.43

Broadsheet

8.96

8.61

From this I can see that the results vary a little bit but the Broadsheet still only has a longer sentence length by a small gap, but the Tabloid has a larger deviance from the mean.

Going Back to The Hypothesis

The first thing I have to ask is, have I proved the hypothesis from my investigation. Well yes and no. My Prediction was that broadsheets have longer sentences making them a harder read. The broadsheets did have longer sentences but does that make them a harder read? My results were very similar, why could this be? Is it because they are at the same reading level, or because sentence length makes no difference to the readability or maybe because I got a harder tabloid or easier broadsheet. I think if I did this again I would have to do 1 of 3 things:

* Introduce another broadsheet and another tabloid.

* Look at something else and not the sentence length.

Or

* Get more samples.

Improvements

If I did do it again I would probably look at something else. I would maybe use the fog index, to find how easy they are to read, or maybe even use the reading age formula, to find out the reading age of each article ad paper. I think using that method would get a more accurate and definite result than the method I used this time. But I cannot ignore the fact that I found what I was aiming to find and had predicted correctly, even if the results were only marginally different.

Even though the margin was slim I did prove my hypothesis.