This Test: 21 pts possible This Question: 1 pt 1 of 21 (0 complete) v How many p
ID: 3178948 • Letter: T
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This Test: 21 pts possible This Question: 1 pt 1 of 21 (0 complete) v How many points do teams score in the championship game of a certain sport? The total numbers of points scored by both teams in each of the first 46 championship games are shown below. Complete parts a through c below 46, 46, 23, 31, 28, 26, 21. 31, 22, 38, 46, 37, 67, 51, 36, 46, 43, 48, 55, 56, 59, 51, 37, 65, 39, 61, 69,42,75, 45, 56, 56, 52,40, 42, 38, 69, 60, 45, 30, 46, 31, 49, 48, 55, 38 a) Find the median. The median is IType an integer or a decimal. Do not round.) b) Find the quartiles. The lower quartile is The upper quartile is IType integers or decimals. Do not round.) c) Write a description based on the 5-number summary. The 5-number summary is T. IType integers or decimals. Do not round. Use ascending order.) In the championship game, teams typically score a total of about points, with half the games totaling more than but less than points. In only one fourth of the games have the teams scored fewer than points, and the most the teams ever totaled was points. NType integers or decimals. Do not round.)Explanation / Answer
1. Median
The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.
Ordering the data from least to greatest, we get:
21 22 23 26 28 30 31 31 31 36 37 37 38 38 38 39 40 42 42 43 45 45 46 46 46 46 46 48 48 49 51 51 52 55 55 55 56 56 59 60 61 65 67 69 69 75
As you can see, we do not have just one middle number but we have a pair of middle numbers, so the median is the average of these two numbers:
Median=46+46/2=46
The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers.So, to find the first quartile, we need to place the numbers in value order and find the bottom half.
21 22 23 26 28 30 31 31 31 36 37 37 38 38 38 39 40 42 42 43 45 45 46 46 46 46 46 48 48 49 51 51 52 55 55 55 56 56 59 60 61 65 67 69 69 75
So, the bottom half is
21 22 23 26 28 30 31 31 31 36 37 37 38 38 38 39 40 42 42 43 45 45 46
The median of these numbers is 37.
The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the upper half.
21 22 23 26 28 30 31 31 31 36 37 37 38 38 38 39 40 42 42 43 45 45 46 46 46 46 46 48 48 49 51 51 52 55 55 55 56 56 59 60 61 65 67 69 69 75
So, the upper half is
46 46 46 46 48 48 49 51 51 52 55 55 55 56 56 59 60 61 65 67 69 69 75
The median of these numbers is 55.
The interquartile range is the difference between the third and first quartiles.
The third quartile is 55.
The first quartile is 37.
The interquartile range = 55 - 37 = 18.
The minimum is the smallest value in a data set and the maximum is the greatest value in a data set.
Ordering the data from least to greatest, we get:
21 22 23 26 28 30 31 31 31 36 37 37 38 38 38 39 40 42 42 43 45 45 46 46 46 46 46 48 48 49 51 51 52 55 55 55 56 56 59 60 61 65 67 69 69 75
So, the minimum is 21 and maximum is 75.
Hence Five summary is Min Q1 Q2 Q3 Max
21 37 46 55 75
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