pages in book 1: 256
pages in book 2: 384
pages in book 3: 31
pages in book 4: 24
pages in book 5: 384
pages in book 6: 64
pages in book 7: 45
pages in book 8: 33
pages in book 9: 22
pages in book 10: 59
pages in book 11: 144
pages in book 12: 273
pages in book 13: 171
pages in book 14: 88
pages in book 15: 15
find the Mean,Median,Mode,Range,IQR and MAD
3 answers
Sorry, I cannot provide you the calculations without the data or numbers. Please provide the necessary details.
Mean:
To find the mean, we need to add up the total number of pages in all the books and divide it by the number of books.
Total number of pages: 256 + 384 + 31 + 24 + 384 + 64 + 45 + 33 + 22 + 59 + 144 + 273 + 171 + 88 + 15
= 1899
Number of books: 15
Mean = 1899/15 = 126.6
Median:
The median is the middle value when the data is placed in numerical order.
Arranging the number of pages in increasing order, we get:
15, 22, 24, 31, 33, 45, 59, 64, 88, 144, 171, 256, 273, 384, 384
The middle value is the average of the 7th and 8th value:
Median = (45 + 59)/2 = 52
Mode:
The mode is the value that appears most frequently in the data set.
In this case, there is no value that appears more than once, so there is no mode.
Range:
The range is the difference between the largest and smallest values in the data set.
Range = 384 - 15 = 369
IQR:
The Interquartile Range (IQR) is the difference between the third quartile and the first quartile.
To find the IQR, we first need to find the quartiles.
The first quartile (Q1) is the median of the lower half of the data set.
Arranging the number of pages in increasing order:
15, 22, 24, 31, 33, 45, 59, 64
The median of this set is:
Median = (31 + 33)/2 = 32
The second quartile (Q2) is the median of the entire data set, which we already found to be 52.
The third quartile (Q3) is the median of the upper half of the data set.
Arranging the number of pages in increasing order:
88, 144, 171, 256, 273, 384, 384
The median of this set is:
Median = (256 + 273)/2 = 264.5
IQR = Q3 - Q1 = 264.5 - 32 = 232.5
MAD:
The Mean Absolute Deviation (MAD) is the average distance between each data point and the mean.
To find the MAD, we first need to find the mean, which we already found to be 126.6.
The deviation of each data point from the mean is:
|256 - 126.6| = 129.4
|384 - 126.6| = 257.4
|31 - 126.6| = 95.6
|24 - 126.6| = 102.6
|384 - 126.6| = 257.4
|64 - 126.6| = 62.6
|45 - 126.6| = 81.6
|33 - 126.6| = 93.6
|22 - 126.6| = 104.6
|59 - 126.6| = 67.6
|144 - 126.6| = 17.4
|273 - 126.6| = 146.4
|171 - 126.6| = 44.4
|88 - 126.6| = 38.6
|15 - 126.6| = 111.6
The average distance between each data point and the mean is:
MAD = (129.4 + 257.4 + 95.6 + 102.6 + 257.4 + 62.6 + 81.6 + 93.6 + 104.6 + 67.6 + 17.4 + 146.4 + 44.4 + 38.6 + 111.6)/15
= 97.9
To find the mean, we need to add up the total number of pages in all the books and divide it by the number of books.
Total number of pages: 256 + 384 + 31 + 24 + 384 + 64 + 45 + 33 + 22 + 59 + 144 + 273 + 171 + 88 + 15
= 1899
Number of books: 15
Mean = 1899/15 = 126.6
Median:
The median is the middle value when the data is placed in numerical order.
Arranging the number of pages in increasing order, we get:
15, 22, 24, 31, 33, 45, 59, 64, 88, 144, 171, 256, 273, 384, 384
The middle value is the average of the 7th and 8th value:
Median = (45 + 59)/2 = 52
Mode:
The mode is the value that appears most frequently in the data set.
In this case, there is no value that appears more than once, so there is no mode.
Range:
The range is the difference between the largest and smallest values in the data set.
Range = 384 - 15 = 369
IQR:
The Interquartile Range (IQR) is the difference between the third quartile and the first quartile.
To find the IQR, we first need to find the quartiles.
The first quartile (Q1) is the median of the lower half of the data set.
Arranging the number of pages in increasing order:
15, 22, 24, 31, 33, 45, 59, 64
The median of this set is:
Median = (31 + 33)/2 = 32
The second quartile (Q2) is the median of the entire data set, which we already found to be 52.
The third quartile (Q3) is the median of the upper half of the data set.
Arranging the number of pages in increasing order:
88, 144, 171, 256, 273, 384, 384
The median of this set is:
Median = (256 + 273)/2 = 264.5
IQR = Q3 - Q1 = 264.5 - 32 = 232.5
MAD:
The Mean Absolute Deviation (MAD) is the average distance between each data point and the mean.
To find the MAD, we first need to find the mean, which we already found to be 126.6.
The deviation of each data point from the mean is:
|256 - 126.6| = 129.4
|384 - 126.6| = 257.4
|31 - 126.6| = 95.6
|24 - 126.6| = 102.6
|384 - 126.6| = 257.4
|64 - 126.6| = 62.6
|45 - 126.6| = 81.6
|33 - 126.6| = 93.6
|22 - 126.6| = 104.6
|59 - 126.6| = 67.6
|144 - 126.6| = 17.4
|273 - 126.6| = 146.4
|171 - 126.6| = 44.4
|88 - 126.6| = 38.6
|15 - 126.6| = 111.6
The average distance between each data point and the mean is:
MAD = (129.4 + 257.4 + 95.6 + 102.6 + 257.4 + 62.6 + 81.6 + 93.6 + 104.6 + 67.6 + 17.4 + 146.4 + 44.4 + 38.6 + 111.6)/15
= 97.9
My apologies, here are the numbers:
pages in book 1: 256
pages in book 2: 384
pages in book 3: 31
pages in book 4: 24
pages in book 5: 384
pages in book 6: 64
pages in book 7: 45
pages in book 8: 33
pages in book 9: 22
pages in book 10: 59
pages in book 11: 144
pages in book 12: 273
pages in book 13: 171
pages in book 14: 88
pages in book 15: 15
pages in book 1: 256
pages in book 2: 384
pages in book 3: 31
pages in book 4: 24
pages in book 5: 384
pages in book 6: 64
pages in book 7: 45
pages in book 8: 33
pages in book 9: 22
pages in book 10: 59
pages in book 11: 144
pages in book 12: 273
pages in book 13: 171
pages in book 14: 88
pages in book 15: 15