Question

Find the mean, median, and interquartile for the data set below. Round your answer to the nearest tenth. 27,16,8,5,19,14,22,31,13,5,23,16,8

Answer 1

Answer:

Hence,

Mean=15.9

Median=16

Interquartile=14.5

Step-by-step explanation:

On arranging our data in the increasing order we get the data set as:

5   5   8   8   13   14   16    16    19    22   23   27   31

Now we find the mean as:

$Mean=\dfrac{5+5+8+8+13+14+16+16+19+22+23+27+31}{13}\\\\Mean=\dfrac{207}{13}\\\\Mean=15.92$

Now, we know that the median is the central tendency of the data and lie in the middle of the data.

Hence, by looking at the data we see that the middle value of the data is 16.

Hence, Median=16.

Now, the lower set of data is:

5   5   8   8  13   14

Now, the lower quartile is calculated as:

The middle value of the lower set of data is:

8     8

Hence, the lower quartile $]Q_1$ is middle of 8,8.

i.e. $\dfrac{8+8}{2}=8$

similarly the upper set of data is:

16    19    22   23   27   31.

Similarly the upper quartile is calculated as:

$Q_3=\dfrac{22+23}{2}=22.5$

Hence, interquartile range (IQR) is calculated as:

$Q_3-Q_1=22.5-8=14.5$

Hence,

Mean=15.9

Median=16

Interquartile=14.5

Answer 2

The mean is 15.92, the median is 16, and the interquartile range is 14.5