91Ó°ÊÓ

The mean, median, standard deviation, the first quartile, the third quartile and the IQR.

The mean is one of the measurements of central tendency in statistics. The mean is defined as the total of data values divided by the number of data values. The following is the formula for determining the mean:

Mean $=\mathrm{μ}=\frac{∑x}{N}$

Calculation: We are given below the data.

$Mean=\frac{10856}{6}=1809.3$

First arrange the data in the ascending order

$1585,1690,1735,1890,1935,2021$

Since we have even number of observations, therefore, the median is:

Median $=\frac{1735+1890}{2}=1812.5$

Hence the median value is = 1812.5

$\begin{array}{rl}\text{Standard deviation}& =\sqrt{\frac{(1585−1809.3{)}^2+(1690−1809.3{)}^2+…+(1890−1809.3{)}^2}{6}}\\ SD& =\sqrt{\frac{50310.49+14232.49+…+137193.3}{6}}\\ SD& =151.2\end{array}$

First we have to arrange the data in ascending order.

$1585,1690,1735,1890,1935,2021$

$Q_1=1690$because it is middle term of the first $50\%$of the data

$Q_3=1935$because it the middle term of the last $50\%$of the data

Now, the interquartile range is calculated as:

$IQR=Q_3-Q_1=1935-1690=245$

Mean$=1809.3$

Median$=1812.5$

Standard deviation =$=151.2$$=151.2$

First quartile$=1690.$

Third quartile$=1935$

$\mathrm{IQR}=245$