Water samples are collected from ten different locations along a beach, eight di

Question

Water samples are collected from ten different locations along a beach, eight different slides of bacterial cultures are prepared from each water sample, and the number of bacteria on the slides is counted. The following table gives the resulting count data:

105      97        245      163      207      134      218      199

160      196      221      154      228      131      180      178

157      151      175      201      183      153      174      154

190      76        101      142      149      200      186      174

199      115      193      167      171      163      87        176

121      120      181      160      194      184      165      145

160      150      181      168      158      208      133      135

172      171      237      170      180      167      176      158

156      229      158      148      150      118      143      141

110      133      123      146      169      158      135      149

(1) Find the (sample) mean of the bacterial count.

            You may wish to try the MATLAB function mean(x).

(2) Find the (sample) standard deviation of bacterial count.

            You may wish to try the MATLAB function std(x)

(3) Find the range (i.e., the maximum and the minimum values) of the bacterial count.

            You may wish to try the MATLAB functions max(x), min(x), and range (x).

(4) Divide the range into N = 10 equal-length segments (hereafter called “bins”), and for each bin, find its bounds (aj, bj) as well as its center cj.

(5) Place each measured bacterial count xi into that bin whose lower bound is less than or equal to xi and whose upper bound is greater than xi; thereafter, for each bin count the number of xi assigned to it (= nj).

(6) Plot a histogram of the measured bacterial counts using N = 10 bars.

            Try the MATLAB functions hist(x,N) and bar(c, n)

(7) Produce a vector Y of measured bacterial counts in which the counts are arranged in ascending order.

(8) Determine the median of measured bacterial counts (at the center of the sorted vector Y) by writing a script that is usable for both odd and even number of samples.

            Try the MATLAB function median(x).

(9) Define a random variable as the bacterial count on a single slide, and estimate (i.e., determine approximately) the probability mass function of this random variable evaluated at the bin centers cj.

(10) Estimate the (cumulative) probability distribution function of the same random variable, evaluated at the same points (i.e. argument values) cj.

            Try the MATLAB function cumsum(nj/Snj).

(11) Produce a plot of the cumulative probability distribution function (found above) as a function of its argument, in which the plot has a title, axes have a scale and a label, and the graph is piece-wise linear between points.

(12) Plot both the histogram and the cumulative probability distribution function in a single graph.

PLEASE TURN IN BOTH YOUR SCRIPT AND THE SOLUTIONS AND PLOTS

So far I have 1-8 done, but I need help at step 9. Is the random variable supposed to be the height of the values for the histogram? How should I code this to be centered at cj?

Explanation / Answer

Using Excel we can find mean standard deviation ,and range :

First plug your given data in one column.

mean = avrage (A1: A80) = 162.66

standard deviation = stdev(A1:A80) = 33.77

Range = max(A1:A80) - min(A1:A80) = 245 - 76 = 169

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