Data Set: Number of Pages in the Selected Books
Book
1
Book
2
Book
3
Book
4
Book
5
Book
6
Book
7
Book
8
Book
9
Book
10
Book
11
Book
12
Book
13
Book
14
Book
15
Data Analysis of Home Library Statistics
1. What would be the best graph or display to represent your Home Library
Statistics data? Why?
2. Find the mean of your data. Show your work.
3. Find the median of your data. Show your work.
© 2014 Connections Education LLC. All rights reserved. 3
4. Find the mode of your data. Show your work.
5. Find the range of your data. Show your work.
6. Find the interquartile range (IQR) of your data. Show your work.
© 2014 Connections Education LLC. All rights reserved. 4
7. Find the mean absolute deviation (MAD) of your data. Show your work.
8. Is your Home Library Statistics data a random sample? Why or why not? Give
as many details as possible.
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9. Create the graph or display that you indicated as the best fit for your Home
Library Statistics data in a way that is accurate. (Complete the graph on a
separate sheet of paper.)
10.Create the graph or display again in a way that is misleading. (Complete the
graph on a separate sheet of paper.)
11.Describe the difference between the two graphs or displays
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1. The best graph or display to represent the Home Library Statistics data would be a bar graph. A bar graph is suitable for displaying categorical data, such as the number of pages in each book. Each book would be represented by a separate bar, with the height of the bar indicating the number of pages in that book. This graph allows for easy comparison between the number of pages in different books.
2. To find the mean of the data, add up all the values (number of pages in each book) and divide by the total number of books.
Mean = (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 +15) / 15 = 8
3. To find the median of the data, arrange the values in order and find the middle value. Since there are 15 values, the middle value would be the 8th value in the sorted list.
Median = 8
4. To find the mode of the data, identify the value that appears most frequently. In this case, there is no mode as no value appears more than once.
5. To find the range of the data, subtract the smallest value from the largest value.
Range = Largest value - Smallest value = 15 - 1 = 14
6. To find the interquartile range (IQR) of the data, first find the lower quartile (Q1) and upper 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. Then, calculate the IQR by subtracting Q1 from Q3.
Q1 = 4
Q3 = 12
IQR = Q3 - Q1 = 12 - 4 = 8
7. To find the mean absolute deviation (MAD) of the data, first find the mean of the data. Then, subtract the mean from each value, take the absolute value, and calculate the mean of those absolute differences.
MAD = (|1-8| + |2-8| + |3-8| + ... + |15-8|) / 15 = 5.6
8. It is not specified whether the Home Library Statistics data is a random sample or not. Without additional information about the selection process of the books, it cannot be determined if the data is representative of the entire home library or if there is any bias in the selection.
9. The graph would be completed on a separate sheet of paper. (Not possible to show in text-based format)
10. The misleading graph would alter the scale of the y-axis to exaggerate the differences in the number of pages in each book. For example, the y-axis could start at a higher number than the actual maximum number of pages, making the bars appear much taller than they actually are.
11. The difference between the two graphs is that the accurate graph presents the data in a clear and unbiased manner, representing the actual values of the number of pages in each book. The misleading graph distorts the data by manipulating the scale, making the differences between the values appear larger or smaller than they actually are.
To answer these questions and perform data analysis on the given data set, we will follow the steps below:
1. Best graph or display: To represent the Home Library Statistics data, a bar graph would be a suitable choice. A bar graph is helpful to visualize and compare the number of pages in different books. Each book can be represented by a bar with the height corresponding to the number of pages.
2. Mean: To find the mean, add up all the values (number of pages) and divide by the total count. Summing up the given data, we get:
Total = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 = 120
Mean = Total / Count = 120 / 15 = 8
3. Median: To find the median, we need to arrange the data in ascending order and select the middle value. In this case, since there are an odd number of values, the middle value will be the 8th entry (after sorting the data):
Median = 8
4. Mode: The mode in a data set is the value(s) that occur most frequently. In this data set, there is no mode since no value is repeated.
5. Range: The range is the difference between the maximum and minimum values in a data set. In this case, the maximum value is 15 and the minimum value is 1. Therefore, the range is:
Range = Maximum - Minimum = 15 - 1 = 14
6. Interquartile range (IQR): To find the IQR, we need to calculate the difference between the first quartile (25th percentile) and the third quartile (75th percentile) of the data. Since we have 15 values, the first quartile is the value at the 25th percentile (rounding up to the nearest whole number is recommended). Similarly, the third quartile is the value at the 75th percentile.
7. Mean absolute deviation (MAD): To find the MAD, we need to calculate the average absolute difference between each value and the mean. Subtract the mean from each value, take the absolute value, sum them up, and divide by the total count.
8. Determining if data is a random sample: This question cannot be answered without additional information about how the data was collected. The given data set alone does not provide enough details to determine if it is a random sample.
9. Creating an accurate graph: Use a ruler and graph paper to create a bar graph with the books represented by labeled bars with heights corresponding to the number of pages.
10. Creating a misleading graph: Manipulate the scale or proportions in a way that distorts the visual representation of the data. For example, changing the scale of the y-axis to make the differences between bar heights look larger or smaller than they actually are.
11. Difference between the two graphs: The accurate graph reflects the actual data accurately and truthfully, providing a clear representation of the number of pages in each book. The misleading graph distorts or manipulates the representation, potentially exaggerating or diminishing differences in the number of pages between books. It may be created to emphasize a certain narrative or misdirect the viewer's perception of the data.