A manager of an inter-county hurling team is concerned that his team lose matches because they ‘fade away’ in the last ten minutes. He has measured GPS data showing how much ground particular players cover within a given time period; this is the data in list (a) in worksheet ‘Dataset3’. He has acquired the corresponding data from an opposing, more successful team, given in list (b). 1. Calculate the sample mean and sample standard deviation for the two sets of data. 2. Set up the frame work of an appropriate statistical test to determine whether there is a difference in the distances covered by the two groups of players. 3. Explain how having the results of the calculations above will influence the structure of your statistical test. 4. Carry out the statistical test and state your conclusions. List (a) List (b) 1491.35 1474.53 1473.56 1563.14 1555.88 1483.87 1507.05 1473.34 1464.63 1497.54 1519.11 1503.03 1483.35 1500.76 1472.52 1494.39 1465.47 1571.51 1537.38 1503.28 1519.41 1471.27 1446.92 1510.30 1530.45 1520.84 1464.34 1490.69 1462.03 1475.84 1484.41 1552.87 1519.60 1492.25 1497.83 1455.37 1438.24 1505.82 1541.67 1517.38 1453.94 1504.70 1480.03 1458.90 1489.77 1533.82 1509.00 1493.74 1438.28 1450.09 1515.77 1522.42 1501.29 1473.10 1483.49 1451.46 1445.1

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

A manager of an inter-county hurling team is concerned that his team
lose matches because they ‘fade away’ in the last ten minutes. He
has measured GPS data showing how much ground particular players
cover within a given time period; this is the data in list (a) in worksheet
‘Dataset3’. He has acquired the corresponding data from an opposing,
more successful team, given in list (b).
1. Calculate the sample mean and sample standard deviation for the
two sets of data.
2. Set up the frame work of an appropriate statistical test to determine whether there is a difference in the distances covered by the
two groups of players.
3. Explain how having the results of the calculations above will influence the structure of your statistical test.
4. Carry out the statistical test and state your conclusions.

List (a)							List (b)
1491.35	1474.53	1473.56	1563.14	1555.88	1483.87	1507.05	1473.34	1464.63	1497.54	1519.11	1503.03	1483.35	1500.76
1472.52	1494.39	1465.47	1571.51	1537.38	1503.28	1519.41	1471.27	1446.92	1510.30	1530.45	1520.84	1464.34	1490.69
1462.03	1475.84	1484.41	1552.87	1519.60	1492.25	1497.83	1455.37	1438.24	1505.82	1541.67	1517.38	1453.94	1504.70
1480.03	1458.90	1489.77	1533.82	1509.00	1493.74		1438.28	1450.09	1515.77	1522.42	1501.29	1473.10	1483.49
							1451.46	1445.10	1533.79	1524.82	1489.16	1480.53

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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