Solved: "Find Mean, Median, Mode, sample variance and range..."

jippie771h

Answered question

2021-11-27

Find Mean, Median, Mode, sample variance and range for following set of data:

\begin{array}{cc} x & 0.23 & 0.36 & 0.56 & 0.89 & 0.76 & 0.77 & 0.81 \end{array}

Answer & Explanation

Archie Griffin

Beginner2021-11-28Added 9 answers

Step 1
The mean can be calculated as:
$\overset{―}{x} = \frac{\sum x}{n}$
$= \frac{0.23 + 0.36 + 0.56 + 0.89 + 0.76 + 0.77 + 0.81}{7}$
$= \frac{4.38}{7}$
$= 0.6257$
The data can be arranged in ascending order as:
0.23, 0.36, 0.56, 0.76, 0.77, 0.81, 0.89
Step 2
The median observation can be calculated as:
$M e d i a n = {(\frac{n + 1}{2})}^{t h}$ Observation
$= {(\frac{7 + 1}{2})}^{t h}$ Observation
$= 4^{t h}$ Observation
The 4th observation of the sorted data is 0.76 . thus median is 0.76
Since, no value is repeated the data doesn't have the mode.
Step 3
The sample variance can be calculated as:
$s^{2} = \frac{\sum x_{i}^{2} - n {\overset{―}{x}}^{2}}{n - 1}$
$= \frac{({0.23}^{2} + {0.36}^{2} + {0.56}^{2} + {0.89}^{2} + {0.76}^{2} + {0.77}^{2} + {0.81}^{2}) - 7 {(0.6257)}^{2}}{7 - 1}$
$= \frac{3.1148 - 2.7406}{6}$
$= 0.0624$
Thus, the sample variance is 0.0624
Range can be calculated as:
$R a n g e = M a x i m u m - M i n i m u m$
$= 0.89 - 0.23$
$= 0.66$

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