Question

FF1 - Please be neat and clear so that I can follow through. Thank You and Thumps Up.

Answer 1

Solution: The following data shows ages of musicians who performed at a concert.

Calculate the Mean, Median and Standard Deviation for these data.

Answer: Let's first find the Mean of the given data:

The formula for Mean is:

$Mean=\frac{\sum_{i=1}^{n}x_{i}}{n}$

$=\frac{22+82+27+43+19+47+41+34+34+42+35}{11}$

   $=\frac{426}{11}$

$=38.7273$ rounded to four decimal places

Therefore, the Mean of the given data is

Now let's find the Median.

To find the Median, we need to first arrange the data in ascending order. The data in ascending order is given below:

Now we have:

$Median=\left ( \frac{n+1}{2} \right )^{th}term$

$=\left ( \frac{11+1}{2} \right )^{th}term$

$=\left ( \frac{12}{2} \right )^{th}term$

$=6^{th}term$

$=35$

Therefore, Median of the given data is

Now let's find the Standard deviation of the given data.

The formula for standard deviation is given below:

$Standard-Deviation=\sqrt{\frac{\sum (x_{i}-\bar{x})^{2}}{n-1}}$

Where $\bar{x}$ is the Mean

Therefore the Standard deviation is:

$Standard-Deviation=\sqrt{\frac{2840.182}{11-1}}$

   $=\sqrt{\frac{2840.182}{10}}$

   $=16.8528$

Therefore, the Standard Deviation of the given data is