Data Set: Number of Pages in the Selected Books
Book
Book Title
Number of Pages (in book)
1
Trials of Apollo: The Hidden Oracle
416
2
Trials of Apollo: The Dark Prophecy
432
3
Trials of Apollo: The Burning Maze
464
4
Trials of Apollo: The Tyrant’s Tomb
448
5
Trials of Apollo: Tower of Nero
434
6
Heroes of Olympus: Son of Neptune
560
7
Heroes of Olympus: Mark of Athena
672
8
Heroes of Olympus: House of Hades
720
9
Heroes of Olympus: Blood of Olympus
554
10
The Sun and the Star
481
Using the information given, answer the next eight questions;
What would be the best graph or display to represent your Home Library Statistics data? Why? (2 points)
Find the mean of your data. Show all the steps. (4 points)
Find the median of your data. Provide explanation. (3 points)
Find the mode of your data. Provide explanation. (2 points)
Find the range of your data. Show all the steps. (2 points)
Find the interquartile range (IQR) of your data. Show all the steps. (4 points)
Find the mean absolute deviation (MAD) of your data. Show all the steps. (8 points)
Is your Home Library Statistics data a random sample? Why or why not? Give as many details as possible. (2 points)
The best graph or display to represent the Home Library Statistics data would be a bar graph or a histogram. This is because the data is categorical (book titles) and has corresponding numerical values (number of pages). A bar graph or histogram would allow for a visual comparison of the number of pages in each book and make it easy to see any patterns or trends in the data.
To find the mean of the data, we need to add up all the values and divide by the total number of values:
(416 + 432 + 464 + 448 + 434 + 560 + 672 + 720 + 554 + 481) / 10 = 4761 / 10 = 476.1
Therefore, the mean of the data is 476.1.
To find the median of the data, we need to arrange the values in order from least to greatest and find the middle value:
416, 432, 434, 448, 464, 481, 554, 560, 672, 720
Since there are 10 values, the middle value is the 5th value, which is 464. Therefore, the median of the data is 464.
The mode of the data is the value that appears most frequently. In this data set, there are no repeated values, so there is no mode.
The range of the data is the difference between the largest and smallest values:
720 - 416 = 304
Therefore, the range of the data is 304.
To find the interquartile range (IQR) of the data, we need to first find the first quartile (Q1) and the third quartile (Q3). Q1 is the median of the lower half of the data, and Q3 is the median of the upper half of the data.
Lower half of the data: 416, 432, 434, 448
Upper half of the data: 560, 672, 720
Q1 = median of lower half = (434 + 448) / 2 = 882 / 2 = 442
Q3 = median of upper half = (560 + 672) / 2 = 1232 / 2 = 616
IQR = Q3 - Q1 = 616 - 442 = 174
Therefore, the interquartile range (IQR) of the data is 174.
To find the mean absolute deviation (MAD) of the data, we first need to find the mean of the data, which is 476.1. Then, we need to find the absolute deviation for each value by subtracting the mean from each value and taking the absolute value. Finally, we need to find the mean of these absolute deviations.
|416 - 476.1| = 60.1
|432 - 476.1| = 44.1
|464 - 476.1| = 12.1
|448 - 476.1| = 28.1
|434 - 476.1| = 42.1
|560 - 476.1| = 83.9
|672 - 476.1| = 195.9
|720 - 476.1| = 243.9
|554 - 476.1| = 77.9
|481 - 476.1| = 4.9
Mean absolute deviation (MAD) = (60.1 + 44.1 + 12.1 + 28.1 + 42.1 + 83.9 + 195.9 + 243.9 + 77.9 + 4.9) / 10 = 792.9 / 10 = 79.29
Therefore, the mean absolute deviation (MAD) of the data is 79.29.
The Home Library Statistics data is not a random sample because it is a specific set of books selected by the individual who collected the data. It does not represent a random sampling of all books, and therefore cannot be generalized to the entire population of books.