Question

Find the range and standard deviation of the set of data. 46​, 44​, 49​, 39​, 48​, 40​, 42

Answer 1

Answer:10,3.58

Step-by-step explanation:

The range of a data set is the difference between the least number and highest number in the data set.

The least number in the data set is $39$.

The highest number in the data set is $49$.

So,range is $49-39=10$

Standard deviation measures how spread out the values in a data set are around the mean.

Let $m$ be the mean of the set.

$m=\frac{46+44+49+39+48+40+42}{7}=\frac{308}{7}=44$

$variance=\frac{(46-44^{2})+(44-44^{2})+(49-44^{2})+(39-44^{2})+(48-44^{2})+(40-44^{2})+(40-44^{2})+(42-44^{2})}{7} =\frac{4+25+25+16+16+4}{7}=12.85$

$standard deviation=\sqrt{variance}=\sqrt{12.85}=3.58$