Concept explainers
a.
To Graph : To construct a histogram for each set of data.
a.
Explanation of Solution
Given information : Given data is,
K’s distance: 17.2, 18.28, 17.28, 17.36, 18.08, 17.43, 17.71, 17.46, 18.26, 17.51, 17.58, 17.41, 18.21, 17.34, 17.63, 17.55, 17.26, 17.18, 17.78, 17.51, 17.83, 17.92, 18.04, 17.91
M’s distance: 18.88, 19.24, 17.63, 18.96, 18.19, 18.21, 18.46, 17.47, 18.49, 17.86,
18.93, 18.73, 18.34, 18.67, 18.56, 18. 79, 18.47, 18.84, 17.94, 18.7
Graph :
For K’s Distances
For M’s Distances
Interpretation :
Both the graphs are unstable. Values are increasing and decreasing.
b.
To describe the center and spread the data using five-number summary.
b.
Answer to Problem 5CYU
TheK’s Distances five number summary is,
Minimum=17.18
Lower quartile=17.38
Median=17.58
Upper quartile=18
Maximum=18.56
The M’s Distances five number summary is,
Minimum=17.74
Lower quartile=18.06.
Median=18.56
Upper quartile=18.85
Maximum=19.24
Explanation of Solution
Given information: Given data is,
K’s distance: 17.2, 18.28, 17.28, 17.36, 18.08, 17.43, 17.71, 17.46, 18.26, 17.51, 17.58, 17.41, 18.21, 17.34, 17.63, 17.55, 17.26, 17.18, 17.78, 17.51, 17.83, 17.92, 18.04, 17.91
M’s distance: 18.88, 19.24, 17.63, 18.96, 18.19, 18.21, 18.46, 17.47, 18.49, 17.86,
18.93, 18.73, 18.34, 18.67, 18.56, 18. 79, 18.47, 18.84, 17.94, 18.7
Formula used: Median is,
Lower quartile is,
Upper quartile is,
Where, n is total number of terms.
Calculation:
Re-arranging the data in an ascending order,
K’s Distances |
17.18,17.2,17.26,17.28,17.34,17.36,17.41,17.43,17.46,17.51,17.51,17.55,17.58,17.63,17.71,17.78,17.83,17.91,17.92,18.04,18.08,18.21,18.26,18.28,18.56 |
M’s Distances |
17.74,17.47,17.63,17.86,17.92,17.94,18.19,18.21,18.34,18.46,18.47,18.49,18.56,18.61,18.67,18.7,18.73,18.79,18.84,18.87,18.88,18.93,18.96,19.18,19.24, |
For K’s Distances
For median,
Substituting values,
On solving,
Substituting the value,
Hence, Median is 17.58
For lower quartile,
Substituting the values,
On solving,
Hence, adding 6th and 7th to get the answer,
On solving,
Hence, Lower quartile is 17.38
For higher quartile,
Substituting the values,
Onn solving,
Hence, adding 19th and 20th to get the answer,
On solving,
Hence, higher quartile is 18
Minimum is the smallest value of dataset.
Hence, minimum is 17.18.
Maximum is the largest value of the dataset.
Hence, maximum is 18.56.
The five number summary is,
17.18,17.38,17.58,18,18.56
For M’s Distances
For median,
Substituting the values,
On solving,
Substituting the value,
Hence, Median is 18.56
For lower quartile,
Substituting the values,
On solving,
Hence, adding 6th and 7th to get the answer,
On solving,
Hence, Lower quartile is 18.06
For higher quartile,
Substituting the values,
On solving,
Hence, adding 19th and 20th to get the answer,
On solving,
Hence, higher quartile is 18.85
Minimum is the smallest value of dataset.
Hence, minimum= 17.74.
Maximum is the largest value of the dataset.
Hence, maximum= 19.24.
The five number summary is,
17.74,18.06,18.56,18.85,19.24
Five number summary is used, since, it is less time consuming and more efficient.
Chapter 10 Solutions
Algebra 1, Homework Practice Workbook (MERRILL ALGEBRA 1)
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