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  • Level: GCSE
  • Subject: Maths
  • Word count: 2694

Maths coursework: read all about it.

Extracts from this document...

Introduction

Maths coursework: read all about it

Introduction:

I am going to do a piece of coursework called read all about it. It is a statistics coursework where I intent to compare the features of a broadsheet newspaper to the features of a tabloid newspaper. Using skills I have learnt in class I am going to try and prove that one has a longer average word length than the other.

Hypothesis:

The average word length is longer in a broadsheet than a tabloid.

Plan:

I am going to buy a tabloid and a broadsheet newspaper from the same day. It is important to buy them from the same day so I can avoid bias. I am going to buy the times and the daily mail and compare the two, there is no specific reason why I chose these newspapers.

First I will number the articles in each newspaper, I will ensure I number 50 articles.

Using the random button on my calculator to avoid bias, I will look at a particular word in the article. For example, if the calculator displays the number, 0.374 I will look at the third word in the article and count the amount of letters in this word. To avoid bias I will always look at the first number after the decimal point.

...read more.

Middle

32

1 < L < 9

49

9 < L < 11

1

10

10

1 < L < 11

50

11 < L < 13

0

12

12

1 < L < 13

50

13 < L < 15

0

14

14

1 < L < 15

50

total

50

284

MEDIAN: frequency +1  = 50+1 = 25.5

                        2                   2

LOWER QUARTILE: frequency+1 = 50+1 =  13

                                        4                 4

UPPER QUARTILE: lower quartile x 3 = 13x3 = 39

*From this cumulative frequency table, I am now going to create a cumulative frequency graph, which will include the median, and upper and lower quartiles.

*From my cumulative frequency graph (on graph paper) I can see that the mean is higher for the broadsheet than the tabloid. This agrees with my hypothesis.

newspaper

median

Lower quartile

Upper quartile

Inter

-quartile range

broadsheet

5.2

3.6

7.6

4

tabloid

4.4

3.2

5.8

2.6

*I believe that this information would be easier to read if It was in a box and whisker diagram. Therefore I am going to create one displaying this information.

*I believe this box and whisker diagram (graph paper) shows very clearly that the broadsheet has a higher median and higher upper and lower quartiles.

Relative frequency:

The relative frequency is the probability of getting a long or short word from my random samples. Having looked at my results, I have decided that a long word is a word with more than 10 letters whereas a short word is a word made up of 5 or less letters. By using these margins and displaying information in a table I am going to work out the percentage chance of picking a long or short word at random

To find the percentage chance of picking a long or short word at random I will divide the frequency by the total sample size, then times this figure by 100. When I have done this for all the values I will display my results in a table.

newspaper

Percentage chance of getting a long word (10+)

Percentage chance of getting a short word (5-)

broadsheet

16%

48%

tabloid

2%

64%

*This table agrees with my hypothesis, the average word length is longer in a broadsheet. At the same time, the tabloid has a higher percentage of short words than the broadsheet. This backs up my hypothesis even more.

*I had intended to go on to make a stem and leaf diagram but having looked at my results, have realised that this is not appropriate. This is because it will not tell me anything I haven’t already discovered, the other diagrams and tables are enough to tell me that the broadsheet has a longer average word length, this has successfully proven my hypotheses. Also I don’t believe that the scope is large enough to justify making a stem and leaf diagram. With all this in mind I have decided not to do a stem and leaf diagram.

Evaluation and conclusion:

Having done this work I have been able to successfully prove my hypothesis. All the diagrams I have made agree with my hypothesis.

        The cumulative frequency table and graph completely back up my prediction, that the broadsheet has a longer average word length. From looking at my graph I can clearly see this but I decided that it would be easier to read if it was displayed in a box and whisker diagram. By looking at the both of these diagrams I can clearly see that the broadsheet has a higher median and a higher lower and upper quartile. I am pleased with this because it helps to prove my hypothesis and my prediction

From my cumulative frequency graph (on graph paper) I can see that the mean is higher for the broadsheet than the tabloid. This agrees with my hypothesis.

I believe this box and whisker diagram (graph paper) shows very clearly that the broadsheet has a higher median and higher upper and lower quartiles.

From looking at both of these diagrams I can tell that the broadsheet has a longer average word length but I still didn’t know what the percentage chance of picking a long or short word was. I could see that the broadsheet had a longer average word length from looking at my cumulative frequency and box and whisker diagrams, but I wanted to prove that the percentage chance of picking a long word was higher in a broadsheet. To do this I decided to make a relative frequency table. I am pleased with the way my relative frequency table has worked out because it proved what I had thought, that the percentage chance of picking along word was higher in a broadsheet than in a tabloid.

Not only this, but it also proved that the percentage chance of picking a short word was higher in a tabloid than in a broadsheet. All of this information helps to back up my hypothesis and prediction, that the average word length is higher in a broadsheet than in a tabloid.

        Overall I, by looking at all my work, I can successfully prove that the average word length is higher in a broadsheet than in a tabloid.

To further my knowledge of broadsheets and tabloids, I have decided to do a second hypothesis. The second hypothesis will be related to the first and will be about sentence length instead of word length.

Hypothesis 2:

The average sentence length is higher in a broadsheet than in a tabloid.

Plan:

First I will number the articles in each newspaper, I will ensure I number 50 articles.

Using the random button on my calculator to avoid bias, I will look at a particular sentence in the article. For example, if the calculator displays the number, 0.374 I will look at the third sentence in the article and count the amount of words in this sentence. To avoid bias I will always look at the first number after the decimal point. However if the first number after the decimal point is a zero I will repeat the method until I get a number from 1-9.

I will repeat this process for every numbered article in the newspaper and then record my results, I will do this for both the broadsheet and the tabloid.

Having done all this I will compile more graphs and tables, much like I did for the first hypothesis. However I am not going to go into such detail in my second hypothesis, I am only going to create a cumulative frequency graph and a box and whisker diagram. I am hoping this will be enough to prove my second hypothesis. Of course, if this isn’t enough I will go into more detail, perhaps making a stem and leaf diagram and possibly a relative frequency table.

Collecting the number of words in every sentence of the newspaper would be too difficult and time consuming.

Therefore I am going to need to sample my sentences. To do this I am going to use the random button on my calculator. I will then be able to take a random sentence and record my results fairly, avoiding bias. For my first hypothesis I used a sample size of 50 however for my second hypothesis I am going to use a sample size of 30.

I predict that the broadsheet will have a longer average sentence length than the tabloid.  

Data collecting:

Broadsheet:

Number of words

tally

frequency

1 < L < 3

0

3 < L < 5

1

5 < L < 7

4

7 < L < 9

8

9 < L < 11

10

11 < L < 13

6

13 < L < 15

1

...read more.

Conclusion

newspaper

median

Lower quartile

Upper quartile

Inter

-quartile range

broadsheet

21

16

25

9

tabloid

14.5

11

18

7

*However I believe it would be easier to read if it was displayed in a box and whisker diagram.

*The box and whisker diagram (graph paper) was also a success and I find it much easier to read than the cumulative frequency graph, it clearly shows that the broadsheet has a longer average sentence length and this agrees with my hypothesis.

*The difference between the two papers is even larger for my second hypothesis.

Evaluation and conclusion:

Having done all this work I have been able to prove my hypothesis. I have also been able to prove my prediction was right. I have been able to display lots of different information in many different diagrams and tables. All of which have helped me prove my hypothesis.

        As I have done two hypotheses’ I have been able to come to a general conclusion. The first hypothesis proved that the average word length was larger in a broadhsheet. The second hypothesis proved that the average sentence length is larger in a broadsheet. By looking at both these results I have been able to see that a broadsheet newspaper has a more intelligent content than a tabloid.

If did this investigation again I think I would use a larger sample size, this would enable me to use a larger variety of methods to prove my hypothesis, for example, I couldn’t do a stem and leaf diagram because I felt the scope wasn’t large enough.

...read more.

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