Find the minimum, first quartile, median, third quartile, and maximum of each data set. Draw the box-and-whisker plot.55 62 61 54 68 72 59 61 70

We can find the median for this set as follows: we have nine (9) elements (odd number of elements) from the list, then, the median is the central value among these elements:

{54, 55, 59, 61, 61, 62, 68, 70,72}

Then, the median is 61 since, in the list, there are four values before it, and four values above it (that is 50% of the values are above and below this point).

Median: 61

The first quartile is the value for which 25% are below it and 75% of the values are above it. In the given data, we have four values below the median. We can get the two central values of them, and then take their mean. That is:

{54, 55, 59, 61}

We take:

(55 + 59) / 2 = 57.

Then, the first quartile is 57.

First Quartile: 57

We can do a similar procedure to find the third quartile:

{62, 68, 70, 72}

(68 + 70}/2 = 69.

Then, the third quartile is 69.

The third quartile is the value for which 75% of the values are lower than it and 25% of the values are above it.

The maximum is the highest value in the set, that is, 72.

Maximum: 72

We can draw this information in the box-and-whisker plot:

We can see from the plot that the minimum is 54, 57 is the first quartile, 61 is the median, 69 is the third quartile, and 72 is the maximum for the given data.