Question

The following data are the temperatures of effluent at discharge from a sewage treatment facility on consecutive days: Sample No.1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Temperature 40 45 49 47 52 45 51 46 44 48 51 50 56 44 48 50 49 50 46 46 49 49 51 50 Use the data above to calculate the descriptive statistics.

Answer 1

The descriptive statistics for the above data is given as follows:
X = 12.5

What is Descriptive Statistics?

A set of concise descriptive coefficients that describe a particular data set indicative of a whole or sample population is known as descriptive statistics.

For X (mean) = ${\displaystyle X={\frac {1}{n}}\sum _{i=1}^{n}X_{i}$

= 300/24

= 12.5

For sample variance = $s^2 = \frac{1}{n-1}\biggl[\, \sum_{i=1}^n X_i^2 - \frac{\Bigl(\,\sum\limits_{i=1}^n X_i\Bigr)^{\!2}}{n} \biggr]$

= (1/(24-1) (4,900 - (300²/24)

= 50

Standard deviation s = √s²

= √50

= 7.0711

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