Question

The following stem-and-leaf plot represents the times in minutes required for 26 co-workers to commute to work. Use the data provided to find the quartiles. Commute Times in Minutes Stem Leaves 2 1 3 5 5 5 8 3 1 5 6 7 8 9 4 2 3 4 6 6 6 8 5 2 2 4 5 7 7 8 Key: 2|1

Answer 1

Answer:

Q1 = 30.25 minutes

Q2 = 42.5 minutes

Q3 = 40 minutes  

Step-by-step explanation:

Given, In Question

• The stem and leaf diagram (key 2 I 1)

Stem | Leaves

2        |  1 3 5 5 5 8

3        |  1 5 6 7 8 9

4        |  2 3 4 6 6 6 8

5        |  2 2 4 5 7 7 8

• We need to find the quartiles Q1, Q2 and Q3. We know that,

Q1 = (1/4)*(n+1)th value

Q2 = (1/2)*(n+1)th value

Q3 = (3/4)*(n+1)th value

where n is the total number of co-workers 26.

• So, Q1 = (1/4)*(26+1)th value

             Q1 = 6.75th value

we need to count the leaves in the plot starting from the first one until we reach the 6.75th value. So, by counting, we conclude that the 6.75th value lies between the 6th and 7th value i.e. 28 and 31.

Q1 = 28 + (31-28)*0.75

    = 28 + 2.25

Q1 = 30.25 minutes

• Now, Q2 = (1/2) * (26+1)th value

                       = 13.5th value.

From the plot, we find that the 13.5th value lies in the middle of the 13th and 14th values i.e. 42 and 43. So,

Q2 = (42+43)/2

     = 85/2  

Q2 = 42.5 minutes

• And, Q3 = (3/4)*(26+1)th value

                      = 20.25th value

From the plot. we find that the 20.25th value lies somewhere between the 20th and 21st value i.e. 52 and 52. So,

Q3 = 40 + (52-52)*0.25

    = 40 + 0

Q3 = 40 minutes