Answer: kindly check Explanation
Step-by-step explanation:
1948 Olympics: Men's 100m Freestyle swim finals
57.3, 57.8, 58.1, 58.3, 58.3, 59.3, 59.6, 65
Lower quartile (Q1) : 1/4(n+1)th term
Where n = number of observations
Q1 = 1/4(8+1)th term
Q1 = 9/4 = 2.25 term
Average of 2nd and 3rd term:
(57.8 + 58.1) / 2 = 115.9/2 = 57.95
Median (Q2) :
Q2 = 1/2(n+1)th term
Q2 = 1/2(9)th term
Q2 = 9/2 = 4.5th term
Average of 4th and 5th term:
(58.3 + 58.3) / 2 = 58.3
Upper quartile (Q3) :
Q3 = 3/4(n+1)th term
Where n = number of observations
Q3 = 3/4(8+1)th term
Q3 = 27/4 = 6.75 term
Average OF 6th and 7th term:
(59.3 + 59.6) / 2 = 118.9/2 = 59.45
Interquartile range ( IQR) :
(Q3 - Q1)
59.45 - 57.95 = 1.5
2) 2012 Olympics: Men's 100m Freestyle swim finals
47.52, 47.53, 47.80, 47.84, 47.88, 47.92, 48.04, 48.44
Lower quartile (Q1) : 1/4(n+1)th term
Where n = number of observations
Q1 = 1/4(8+1)th term
Q1 = 9/4 = 2.25 term
Average of 2nd and 3rd term:
(47.53+ 47.80) / 2 = 95.33/2 = 47.67
Median (Q2) :
Q2 = 1/2(n+1)th term
Q2 = 1/2(9)th term
Q2 = 9/2 = 4.5th term
Average of 4th and 5th term:
(47.84 + 47.88) / 2 = 47.86
Upper quartile (Q3) :
Q3 = 3/4(n+1)th term
Where n = number of observations
Q3 = 3/4(8+1)th term
Q3 = 27/4 = 6.75 term
Average OF 6th and 7th term:
(47.92 + 48.04) / 2 = 47.98
Interquartile range ( IQR) :
(Q3 - Q1)
47.98 - 47.67 = 0.31
Range of values in the 2012 Olympics Swim finals are closer to one another than in the 1948 Olympics as shown by the values of the interquartile range.
The athlete's Swim speed seems to have improved drastically from the 1948 Olympics during the 2012 finals as athletes elapsed time have become significantly lower.
