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Answer:
a) s = 8.81
b) Q1 = 43.4, Q2 = 49.4, Q3 = 57.35
c) See below
Step-by-step explanation:
(a) Find the standard deviation of the reflectance for these smolts. (Round your answer to two decimal places.)
In order to find the standard deviation, we need the mean first. The mean is defined as
where the are the values of the data collected and n=50 the size of the sample.
So, the mean is
Now, the standard deviation of the sample is defined as
and we have that our standard deviation is
s = 8.81
(b) Find the quartiles of the reflectance for these smolts
To find the quartiles, we must sort the data from lowest to largest:
33.6, 37.7, 38.3, 38.7, 42, 42, 42.2, 42.4, 42.7, 42.8, 42.9, 43.1, 43.7, 43.8, 44.2, 44.6, 45.5, 45.7, 46.3, 46.6, 47.4, 47.6, 47.7, 47.9, 49.2, 49.6, 50.5, 50.9, 51.3, 53, 53.9, 54.8, 54.9, 55.5, 56, 56, 56.2, 57.1, 57.6, 58.3, 59, 59.5, 60.4, 63.2, 63.4, 63.5, 64.6, 68, 69.1, 69.2
The <em>first quartile</em> is the number between the 12th and the 13th data (so 25% of the data are below it and 75% above it)
So the 1st quartile is
The <em>2nd quartile is the median</em>, the point between the 25th and 26th data, it splits the data in two halves.
The 3rd quartile is the point between the 38th and 39th data (so 75% of the data are below it and 25% above it)
(c) Do you prefer the standard deviation or the quartiles as a measure of spread for these data? Give reasons for your preference.
In this case, we prefer the quartiles as a measure of spread since the data are very scattered around the mean and there is no a central tendency.