Question

Speed of light from galaxies. Astronomers theorize that cold
dark matter (CDM) caused the formation of galaxies. The
theoretical CDM model requires an estimate of the velocity
of light emitted from the galaxy. The Astronomical Journal
(July, 1995) published a study of galaxy velocities. One
galaxy, named A1775, is thought to be a double cluster; that
is, two clusters of galaxies in close proximity. Fifty-one velocity
observations (in kilometers per second, km/s) from
cluster A1775 are listed in the table.

22922 20210 21911 19225 18792 21993 23059
20785 22781 23303 22192 19462 19057 23017
20186 23292 19408 24909 19866 22891 23121
19673 23261 22796 22355 19807 23432 22625
22744 22426 19111 18933 22417 19595 23408
22809 19619 22738 18499 19130 23220 22647
22718 22779 19026 22513 19740 22682 19179
19404 22193

a. Use a graphical method to describe the velocity distribution
of galaxy cluster A1775.
b. Examine the graph, part a. Is there evidence to support
the double cluster theory? Explain.
c. Calculate numerical descriptive measures (e.g., mean
and standard deviation) for galaxy velocities in cluster
A1775. Depending on your answer to part b, you may
need to calculate two sets of numerical descriptive
measures, one for each of the clusters (say, A1775A
and A1775B) within the double cluster.
d. Suppose you observe a galaxy velocity of 20,000 km/s.
Is this galaxy likely to belong to cluster A1775A or
A1775B? Explain.

Answer 1

a) The velocities are distributed as shown in the scatter plot below:

b) There is evidence to support the double cluster theory since the velocities appear to belong to 2 different noticeable clusters. There are 2 parallel, nearly horizontal clusters in the scatter plot above.

c) To cluster the data into 2 sets:

1) we calculate the mean of the overall data set

2) calculate the distance of each point from this mean. This gives us a set of -ve distances and a set of +ve distances.

3) These 2 sets of points which give us -ve and +ve distances respectively, form the 2 clusters.

Mean of A1775A = 19462, Std dev = 532.29

Mean of A1775B = 22838, Std dev = 561

d) A galaxy velocity of 20000 km/s is nearer to the cluster mean of A1775A, hence likely to belong to A1775A