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• Level: GCSE
• Subject: Maths
• Word count: 3118

# Compare children's books and adult's books by setting an appropriate hypothesis and then finding relevant data to prove it.

Extracts from this document...

Introduction

This is my maths statistics coursework, which is called, read all about it. The aim of this coursework is for me to statistically analyse books or newspapers.

## My Plan

My plan is to compare children’s books and adult’s books by setting an appropriate hypothesis and then finding relevant data to prove it. I have decided that my hypothesis will be that there are longer words in adult’s fiction books than in children’s fiction books. I am going to do this by counting the numbers of letters in a word. I am going to use three children’s adventure books and three adult romance books, this is to stop bias and make data more reliable by using more than one book. I am going to use books by different authors this is so as to stop being biased. I am going to use the first one hundred words from the middle page from each book; this is also to stop being bias by using random sampling.

With these words, I will make a tally chart to show the number of letters in each word. From the data I

Middle

9

4

96

10

1

97

11

3

100

##### Leap of Faith
 No of letters in a word Frequency Cumulative Frequency 1 5 5 2 10 15 3 36 51 4 18 69 5 5 74 6 9 83 7 9 92 8 3 95 9 2 97 10 2 99 11 0 99 12 1 100
##### Mr Majeika
 No of letters in a word Frequency Cumulative Frequency 1 4 4 2 21 25 3 19 44 4 19 63 5 10 73 6 12 85 7 8 93 8 4 97 9 2 99 10 1 100
##### Naughty Ameilia Jane
 No of letters in a word Frequency Cumulative Frequency 1 3 3 2 12 15 3 34 49 4 24 73 5 9 82 6 13 95 7 1 96 8 2 98 9 1 99 10 1 100
##### The Hedgehog
 No of letters in a word Frequency Cumulative Frequency 1 3 3 2 19 22 3 32 54 4 14 68 5 18 86 6 9 95 7 3 98 8 1 99 9 1 100

## What I have found From The Tally Charts

By calculating the mean from the data in the tables the mean number of words in the adult’s books is 4.21, 4.24, 4.59, whereas the children’s books have lower means, 3.75, 3.9, and 4.17. This shows that the adult’s books do have on average bigger words but not by much.

The ranges of the adult’s books are 10, 11, 10, whereas the children’s are 8, 9, and 9. This shows that the adult books have a bigger spread of words and the children’s books have a closer spread of word length.

The tables show that the adults books still have a lot of smaller words (2, 3, 4 lettered words) but they have a lot more longer words (8, 9, 10, 11 lettered words) that the children’s books do not have.

## What I have Found from the Cumulative Frequency Graphs and Box Plots

By looking at the cumulative frequency graphs and the box plots it shows that the adult’s books have upper quartiles of 4.6, 6, 5.1 whereas the children’s books have upper quartiles of 4.4, 4.2, and 5.2. Quite clearly overall the adult books have higher upper quartiles.

When looking at the lower quartiles, there doesn’t seem to be much difference between the adults and the children’s. The adult books lower quartiles are 2, 2.2 and 2.2 and the children’s are 2, 1.8 and 2.1. This shows that the adult’s books have lower quartiles are just slightly higher not too much.

The inter quartile ranges of the adults books are 3.1, 3.8 and 2.4. The children’s books are 3, 2.8 and 2. This shows that the adult’s books have a bigger inter quartile range showing that the data is more widely spread about the median. This proves that the adult’s books have larger words than the children’s books.

## What I have found from the Standard Deviation

I have used the “divisor n-1” formula since I am working with a sample data set. The standard deviations of the adult’s books are 15.21, 15.54 and 15.19 and the standard deviation of the children books is 14.13, 16.18 and 15.15. I worked out the mean standard deviation for the adults and the children’s to see which is the largest. The adults mean standard deviation is 15.31 and the children books standard deviation is 15.15. This shows that overall the adults books have a higher standard deviation. This means that the adult books have a wider spread, proving that the adult books have slightly larger words.

## Conclusion

All this information proves that adult books do have longer words than children books but adult books still have quite a few shorter words in them. Although children books have quite long words (7, 8, 9 lettered words) the adult’s longer words are even bigger (9, 10, 11, 12 lettered words). So I have come to the conclusion that my hypothesis is correct.

## Developing my hypothesis

I am now beginning to wonder if the word length also changes the size of sentence length. So to see if this is correct I am going to change my hypothesis to ‘there are sentences in adult fiction books than in children’s fiction books.’

I am going to collect my data from the same books as I used last time on the same page this is again to avoid bias. I am going to take the first 15 sentences from the page and record my results in tally charts and then produce frequency polygons to show my results.

## Data

Lightning strikes

No of words in a sentence

Mid Point

### Tally

Frequency

Fx=

1-5

3

4

12

6-10

8

3

24

11-15

13

3

39

16-20

18

2

36

21-25

23

2

46

26-35

30.5

1

30.5

Total= 187.5

Mean= 12.5                         Mode= 1-5

Median= 11-15

##### The Obsession
 No of words in a sentence Mid Point Tally FrequencyFx= 1-5 3 4 12 6-10 8 7 56 11-15 13 1 13 16-20 18 2 36 21-25 23 1 23 26-35 30.5 0 0

Total= 140

Mean= 9.33                                                Mode= 6-10

Median= 6-10

##### Leap of Faith
 No of words in a sentence Mid Point Tally FrequencyFx= 1-5 3 2 6 6-10 8 3 24 11-15 13 3 39 16-20 18 4 72 21-25 23 2 46 26-35 30.5 1 30.5

Total= 217.5

Mean= 14.5                                                Mode= 16-20

Median= 11-15

## Mr. Majeika

 No of words in a sentence Mid Point Tally FrequencyFx= 1-5 3 5 15 6-10 8 2 16 11-15 13 2 26 16-20 18 3 54 21-25 23 1 23 26-35 30.5 2 61

Conclusion

## Overall Conclusion

From all this information I have came to the strong conclusion that my hypothesis is correct because all the information has pointed to adult books having longer sentences than children books. I have also come to the conclusion that when books have longer words they also have longer sentences. I have come to this conclusion because the adult’s books have the longer words and also have the longest sentences. This also means that children’s books do have shorter words and shorter sentences, which is what you would expect to normally find to help them to learn to read.

Limitations and Improvements

The limitations of this investigation were that we had a limited amount of time and I only had a limited amount of books available to me. So this means that both hypotheses are not conclusive because this is only a small sample taken. To make this investigation better, I could have looked at a wider range of books by lots more different authors, which would have made bias even more unlikely to happen. I would also use more of the data out of the books from more pages; this would also make bias much more unlikely to happen. I could also investigate page length, paragraph length or the amount of pages in a chapter.

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