Question

Directions: Answer the following questions based on your Desmos box plot assignment from Friday:The initial data is:8, 9, 9, 9, 6, 9 , 8, 6, 8, 6, 8 , 8, 8, 6, 6, 6, 3, 8, 8, 9 1) Based on your box plot, identify the following values: Minimum: W Lower Quartile (Q1): Median: Upper Quartile (Q3): Maximum: Interquartile Range (IQR): 2) Based on the box plot, do you expect the mean to be greater than the median value, less than the median value, or the same as the median value? Why? 3) What information do you get from a box plot that you do not get from a histogram? 4) What information to you get from a histogram that you do not get from a box plot? Tot Cintin

Answer 1

Your initial data is:

8, 9, 9, 9, 6, 9 , 8, 6, 8, 6, 8 , 8, 8, 6, 6, 6, 3, 8, 8, 9

To find the minimum, Lower quartile, Medina, Upper quartil, Maximun, and the interquertile range, we need to organize the data as:

3 , 6, 6, 6, 6, 6, 6, 8, 8, 8,

1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th

8, 8, 8, 8, 8, 9, 9, 9, 9, 9

11th 12th 13th 14th 15th 16th 17th 18th 19th 20th

Now, the minimum value is 3

The maximum value is 9

The position of the lower quartile is equal to:

Pos Q1 = (n+1)/4 = (20+1)/4 = 5.25

So, the value at position 5th and 6th is 6. It means that the lower quartile is 6.

At the same way the position of the median and the upper quartile are:

Pos Median = (n+1)/2 = 21/2 = 11.5

It means that the median is 8.

Pos Q3 = 3(n+1)/4 = 3*21/4 = 15.75

In this case the value at position 15th is 8 and the value at position 16th is 9. So, the upper quartile is 8.5

Finally, the IQR can be calculated as:

IQR = Q3 - Q1

IQR = 8.5 - 6 = 2.5

Answer: MInimum: 3

Q1 = 6

Median: 8

Q3 = 8.5

Maximum = 9

IQR = 2.5