Question

box whiskers
lower quartile
q1
median
upper quartile
q3
min
whisker
max
whisker
interquartile range
: the number in the data set shown at the end of the left \whisker.\
: the number in the data set shown at the far right of the box.
: is shown as a line in the box. it represents the value of the data set (50%), but not necessarily drawn in the middle of the box.
: there are quartiles, each interval representing of the data. q1 is, q2 is, q3 is, q4 is
example#13: construct a box plot for the following data: 12, 5, 22, 30, 7, 36, 14, 42, 15, 53, 25
step 1: arrange the data in ascending order.
step 2: find the min, max, and median,
step 3: lower quartile (bottom half)
and upper quartile (top half)
step 4: draw boxes and whiskers. ta - da!
5 10 15 20 25 30 35 40 45 50
example#14
41, 42, 43, 43, 43, 45, 47, 48, 50, 50
which box plot correctly summarizes the data?
example #15
32, 34, 36, 37, 36, 37, 38, 37, 38
34, 38, 34, 37, 32, 32, 39, 34, 39
37, 38, 36, 33, 34, 32, 34, 37, 32
a)
b)
c)

Explanation:

Step1: Define box - plot components

In a box - plot, the minimum value is the smallest number in the data set shown at the end of the left "whisker". The upper quartile (Q3) is the number in the data set shown at the far right of the box. The median is shown as a line in the box and represents the middle value of the data set (50%). There are 4 quartiles, each interval representing 25% of the data. Q1 is the lower quartile, Q2 is the median, Q3 is the upper quartile, and Q4 is the maximum value.

Step2: Solve example #13

Arrange data in ascending order

The data set is 5, 7, 12, 14, 15, 22, 25, 30, 36, 42, 53.

Find min, max, and median

The minimum (min) is 5, the maximum (max) is 53. There are n = 11 data points. The median (Q2) is the 6th - ordered value, so median=22.

Find lower and upper quartiles

The lower half of the data is 5, 7, 12, 14, 15. The lower quartile (Q1) is the 3rd - ordered value of the lower half, so Q1 = 12. The upper half of the data is 25, 30, 36, 42, 53. The upper quartile (Q3) is the 3rd - ordered value of the upper half, so Q3 = 36.

Step3: Solve example #14

Arrange data in ascending order

The data set is 41, 42, 43, 43, 43, 45, 47, 48, 50, 50. There are n = 10 data points.

Find min, max, and median

Min = 41, max = 50. The median (Q2) is the average of the 5th and 6th - ordered values, so Q2=$\frac{43 + 45}{2}=44$.

Find lower and upper quartiles

The lower half is 41, 42, 43, 43, 43. Q1 = 43. The upper half is 45, 47, 48, 50, 50. Q3 = 48.

Step4: Solve example #15

For each data set, we would follow the same steps of arranging in ascending order, finding min, max, median, Q1 and Q3 to determine the correct box - plot. But without specific options for example #15 clearly labeled in the question, we focus on the general concepts and example #14.

Answer:

For example #14, after calculating min = 41, Q1 = 43, Q2 = 44, Q3 = 48, max = 50, we can match with the correct box - plot among the given options (not fully shown in the question but we have the calculated values to make the match). For the blanks in the general description: "minimum: the smallest number in the data set shown at the end of the left 'whisker.'; upper quartile: the number in the data set shown at the far right of the box; median: is shown as a line in the box. It represents the middle value of the data set (50%), but not necessarily drawn in the middle of the box; quartiles: There are 4 quartiles, each interval representing 25% of the data. Q1 is the lower quartile, Q2 is the median, Q3 is the upper quartile, Q4 is the maximum value."