Assignment: Statistical Analysis

Part 1 Optional

Read ‘Cosmic Web' or Cosmic Electricity Grid: Observations on the largescale structure of the Universe over the past decades have given rise to the notion of the ‘cosmic web', which is nothing if not the cosmic electricity grid of the Electric Plasma Universe Dr Mae-Wan Ho (ISIS Report 19/10/15) [http://www.i-sis.org.uk/Cosmic_Web_or_Cosmic_Electricity_Grid.php]

Part 2 Required

The following information is for Problems 1 and 2:

100 random samples were taken from a large population. A particular numerical characteristic of sampled items was measured. The results of the measurements were as follows:

45 measurements were between 0.859 and 0.900
0.901 was observed once
0.902 was observed three times
0.903 was observed twice
0.904 was observed four times
45 measurements were between 0.905 and 0.958

The smallest value was 0.859, and the largest value was 0.958. The sum of all 100 measurements was 91.170. Except those noted, no measurements occurred more than twice.

1) What is the mean of the measurements?

2) What is the mode of the measurements?

3) Muscle fatigue can be measured by means of the frequency spectrum, related to standard deviation, of electrical signals recorded from the muscle. The following is a list of values (in arbitrary units) for the myoelectric signal during isokinetic knee extension using the rectus femoris muscle. Compute the standard deviation of the bold values (by hand) OR all of the values (by computer program).

0.35    0.15     0.70    -0.65    0.28    -0.10
-0.25  -0.24   -0.80     0.16   -0.35    -0.03
-0.10   0.15    0.04     0.00     0.04    0.00
-0.10  -0.13    0.50    0.25      0.08    0.06
 0.08   -0.23   0.22   0.01       0.08     0.01

4) A student received grades 75, 85, 80 and 73 on homework assignments and a final exam grade of 68. If the final exam grade is weighted 4 times that of the homework assignments, what is the student's mean score?

5) What is the sample variance in cfs? [Use the bold values if calculating by hand OR use all values if done by computer program.]

Agency ID      Site Number       Date            Discharge, cubic feet per second         Provisional data subject to revision
  USGS           03431599       2013-06-01                           18                                                       P
  USGS           03431599       2013-06-05                           11                                                       P
  USGS           03431599       2013-06-07                           7.0                                                      P
  USGS           03431599       2013-06-09                           11                                                       P
  USGS           03431599       2013-06-11                           28                                                       P
  USGS           03431599       2013-06-15                           2.5                                                      P
  USGS           03431599       2013-06-17                           101                                                     P
  USGS           03431599       2013-06-21                           6.6                                                      P
  USGS           03431599       2013-06-25                           1.7                                                      P
  USGS           03431599       2013-06-30                           0.49                                                    P