Question

Thirty SCC instructors were asked, "How many minutes does it take for you to commute towork on a typical Wednesday?" The data are listed below:25, 31, 23, 40, 8, 13, 28, 22, 30, 37, 43, 75, 2, 14, 32,31, 25, 14, 12, 24, 28, 35, 25, 50, 16, 12, 9, 38, 11, 22a) Make a stem-and-leat display of the data in the space provided below. You may want tomake a scratch copy, as the leaves' should be written in order on the final copy.

Answer 1

We have to separate the numbers into groups

2, 9, 8

14, 14, 12, 16, 12,11, 13

25, 23, 28, 22, 25, 24, 28, 25, 22

31, 30, 37, 32, 31, 35, 38

40, 43,

50

75

Now we will arrange each group from smallest to greatest

2, 8, 9

11, 12, 12, 13, 14, 14, 16

22, 22, 23, 24, 25, 25, 25, 28, 28

30, 31, 31, 32, 35, 37, 38

40, 43

50

75

Now we will take the ten-digit as stem and the unit-digit as leaf

a)

Stem----Leaf

0. 2, 8, 9

1 1, 2, 2, 3, 4, 4, 6

2. 2, 2, 3, 4, 5, 5, 5, 8, 8

3. 0, 1, 1, 2, 5, 7, 8

4. 0, 3

5. 0

6

7. 5

b)

The median is the middle number

Since we have 30 numbers, then

The median will be the average of the 15th and 16th numbers

Let us find them

The 15th is 25

The 16th is 25

Then the median = (25 + 25)/2 = 50/2 = 25

Median = 25

To find the first quartile we will find the medina of the first 15 numbers

The middle number of 15 numbers is the number in the 8th position

The first 15 numbers are

2, 8, 9, 11, 12, 12, 13, 14, 14, 16, 22, 22, 23, 24, 25

The number in the 8th position is 14

The 1 st quartile is 14

To find the 3rd quartile we will find the median of the last 15 numbers

The last 15 numbers are

25, 25, 28, 28, 30, 31, 31, 32, 35, 37, 38, 40, 43, 50, 75

The median will be the number in the 8th position

The number in the 8th position is 32

The 3rd quartile is 32

The answers are

Median = 25

Q1 = 14

Q3 = 32

C)

To find the interquartile range IQR subtract Q1 from Q3

IQR = 32 - 14 = 18

The answer is

IQR = 18