Word Length Comparison in Classic and Modern Novels

Hypothesis

In classic novels, the words are longer in length than the words in modern fiction.

Introduction

This investigation aims to determine whether the words in classic novels are, on average, longer than those used in modern fiction, as suggested in the hypothesis. The two novels selected for this comparative analysis are the classic novel 'The Lion, The Witch and the Wardrobe' by C.S. Lewis, published in 1950, and the modern fiction novel 'When it Drops' by Alex Dyson, published 50 years later in 2020.

To verify the hypothesis, we will collect tabulated data and perform mathematical calculations based on word lengths from each novel. The data collection method involves using a random sample of 50 words from each book and recording the length of each word in letters. Prior to data collection, we make several assumptions to address potential sources of uncertainty in the experiment:

• We assume that the random number generator feature on the calculator functions randomly, without bias or programmed responses.
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• We exclude pages in the books, particularly those at the immediate front or back, such as the content table, title page, glossary, and author's message, as they typically contain limited vocabulary and do not represent the word choice and writing style of the respective time periods.

It is important to note that due to the classic novel being written 50 years before the modern fiction novel, both novels exhibit distinct vocabulary characteristics. Additionally, the modern novel contains more pages, but it also includes multiple cartoons and employs a larger font size.

To ensure the random selection of words, we have devised a procedure involving mathematical processes.

In this method, we will select one word from 50 different pages in each book. To determine which pages to use in the sample, we will divide the total number of pages in each book by 50. The resulting quotient will guide us in selecting the specific pages for word sampling. On each selected page, we will employ two random numbers to determine both the line and the position of the word that will be sampled. To maintain randomness in data collection, we will apply the appropriate formula to a calculator to generate random numbers, ensuring that the positions of the sampled words are entirely unbiased.

Collecting the Data Samples

Raw Data

Below is the raw data collected from 'The Lion, The Witch and the Wardrobe' and 'When It Drops' for word length comparison:

Table 1: 'The Lion, The Witch and the Wardrobe' Raw Data

Word Number	Word Length
1	8
2	9
3	8
4	3
5	9
6	2
7	7
8	10
9	7
10	8
11	1
12	7
13	6
14	4
15	7
16	2
17	6
18	11
19	7
20	5
21	5
22	6
23	7
24	6
25	9
26	11
27	3
28	5
29	7
30	6
31	10
32	5
33	6
34	7
35	1
36	8
37	10
38	5
39	6
40	6
41	8
42	11
43	7
44	7
45	8
46	10
47	3
48	4
49	8
50	8

Table 2: 'When It Drops' Raw Data

Word #	Word Length
1	6
2	6
3	7
4	8
5	3
6	4
7	4
8	5
9	6
10	7
11	8
12	5
13	6
14	5
15	6
16	7
17	6
18	6
19	7
20	8
21	7
22	6
23	7
24	7
25	4
26	5
27	3
28	4
29	4
30	4
31	4
32	5
33	4
34	5
35	4
36	4
37	5
38	6
39	6
40	6

Data Collection and Analysis

Method to Ensure Randomness

To ensure the collection of random data, we applied the appropriate formula to a calculator to generate random numbers. The product of this calculation provided the position of the word that was used as a sample.

Class Intervals

The class intervals used in this analysis are as follows: 1-2, 3-4, 5-6, 7-8, 9-10, and 11-12.

Displaying the Data Samples

'The Lion, The Witch and The Wardrobe'

Length of Word (letters)	Midpoint	Frequency	fx	cf
1 to 2	1.5	6	9	6
3 to 4	3.5	13	45.5	19
5 to 6	5.5	14	77	33
7 to 8	6.5	13	84.5	46
9 to 10	9.5	2	19	48
11 to 12	11.5	2	23	50
Total		50	258

Table 3: 'The Lion, The Witch and The Wardrobe' Word Length Frequency

'When It Drops'

Length of Word (letters)	Midpoint	Frequency	fx	cf
1 to 2	1.5	3	4.5	3
3 to 4	3.5	6	21	9
5 to 6	5.5	13	71.5	22
7 to 8	6.5	18	117	40
9 to 10	9.5	7	66.5	47
11 to 12	11.5	3	34.5	50
Total		50	315

Table 4: 'When It Drops' Word Length Frequency

Statistical Calculations

Chosen Systematic Sampling Formula

For 'The Lion, The Witch and The Wardrobe', the systematic sampling formula yielded:

Line = Random Number

Word = Random Number

Average = 4.06

Therefore, every 4th page was used for data collection.

For 'When It Drops', the systematic sampling formula yielded:

Line = 15

Word = 6

Average = 6.36

Therefore, every 6th page was used for data collection.

Measures of Central Tendency - 'The Lion, The Witch and The Wardrobe'

Mean:

The mean indicates the average word length in both novels, calculated by summing all word lengths and dividing by the sample size (50). A higher mean suggests longer words on average. The classic novel had a mean word length of 6.3, while the modern fiction novel had an average word length of 5.2 letters. The data supports the hypothesis that classic novels contain longer words.

Median:

The median is the middlemost value in the data set. The classic novel had a higher median word length of 9.33, compared to the modern fiction novel with a median word length of 7.07 letters, supporting the hypothesis.

Mode:

The mode represents the most frequently occurring word length. In the classic novel, the modal class was 7-8, while in the modern fiction novel, it was 5-6. This reaffirms that longer words are more frequent in classic novels.

Range:

The range measures the variation between the highest and lowest values. Both novels had the same range, using identical class intervals, and do not provide evidence for or against the hypothesis.

Interquartile Range (IQR):

The IQR measures the spread of data points from the mean. The classic novel's IQR of 33.93 contrasts significantly with the modern fiction novel's IQR of 1.77. This supports the hypothesis that classic novels contain longer words compared to modern fiction novels.

Observations and Discussion

The graphs of 'The Lion, The Witch And The Wardrobe' and 'When It Drops' display distinct patterns. Both novels have the same class intervals, representing the word length range. It is evident from the graphs that 'The Lion, The Witch And The Wardrobe' exhibits a higher frequency of longer words, reinforcing the hypothesis. The 7-8 class is notably more frequent in the classic novel's graph, and overall, it has higher frequencies of words in the upper classes. Conversely, the modern fiction novel's graph displays higher frequencies of words in the lower classes and fewer in the middle to upper classes. Visual representations and statistical data from the graphs clearly support the notion that classic novels contain longer words compared to modern fiction novels.

Summary

Each statistical measure calculated in this investigation supports the hypothesis that in classic novels, words are longer than in modern fiction. Measures of central tendency, such as mean, median, mode, and interquartile range, consistently indicate that the classic novel has longer word lengths. The only exception is the range, which was identical for both data sets and does not provide evidence for or against the hypothesis. Therefore, all relevant calculations confirm that classic novels indeed feature longer words than those found in modern novels, supporting the hypothesis.

Evaluation

The systematic sampling method, random calculation process, measures of central tendency calculations, and various tables/graphs used in this investigation contribute to its validity. Initial observations and assumptions provided a foundation for the investigation and ensured that all aspects were reasonable. However, the sample size was relatively small, which could affect result accuracy compared to a larger sample. Nonetheless, the investigation's strengths include the methods used, such as systematic sampling, a reliable random number generator, and accurate central measures of tendency. These aspects collectively support the hypothesis. While the results are strong, further research with a larger sample group could enhance the validity of the findings, although it may yield predictable results similar to this investigation.

Conclusion

This investigation, utilizing mathematical calculations, tabulated data, and technology, conclusively confirms the hypothesis that in classic novels, words are longer in length than in modern fiction. The evidence and data generated throughout the investigation firmly support the hypothesis. The combination of appropriate methods used in the procedure results in a conclusive affirmation of the hypothesis's validity. Classic novels consistently feature longer words, providing a compelling confirmation of the hypothesis.

Appendices

'The Lion, The Witch And The Wardrobe'

Length of Word (letters)	Midpoint	f	fx	cf
1 to 2	1.5	3	=C2*D2	3
3 to 4	3.5	6	=C3*D3	=F2+D3
5 to 6	5.5	13	=C4*D4	=F3+D4
7 to 8	6.5	18	=C5*D5	=F4+D5
9 to 10	9.5	7	=C6*D6	=F5+D6
11 to 12	11.5	3	=C7*D7	=F6+D7
Total		=SUM(D2:D7)	=SUM(E2:E7)

'When It Drops'

Length of Word (letters)	Midpoint	Frequency	fx	cf
1 to 2	1.5	6	=I3*J3	6
3 to 4	3.5	13	=I4*J4	=L3+J4
5 to 6	5.5	14	=I5*J5	=L4+J5
7 to 8	6.5	13	=I6*J6	=L5+J6
9 to 10	9.5	2	=I7*J7	=L6+J7
11 to 12	11.5	2	=I8*J8	=L7+J8
Total		=SUM(J3:J8)	=SUM(K3:K8)

Word Length Frequency Summary

'The Lion, The Witch And The Wardrobe'

Length of Word (letters)	Frequency
1 to 2	3
3 to 4	6
5 to 6	13
7 to 8	18
9 to 10	7
11 to 12	3

'When It Drops'

Length of Word (letters)	Frequency
1 to 2	6
3 to 4	13
5 to 6	14
7 to 8	13
9 to 10	2
11 to 12	2