Answer:
Q1 = 18.25 minutes
Q2 = 33.5 minutes
Q3 = 40.75 minutes
Explanation:
The stem and leaf diagram is:
Stem | Leaves
1 | 0 4 4 6 6 6 9
2 | 2 4 4 5 8
3 | 3 4 4 5 6 8
4 | 0 0 3 3 5 6 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. 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. 16 and 19.
Q1 = 16 + (19-16)*0.75
= 16 + 2.25
Q1 = 18.25 minutes
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 value i.e. 33 and 34. So,
Q2 = (33+34)/2
= 67/2
Q2 = 33.5 minutes
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. 40 and 43. So,
Q3 = 40 + (43-40)*0.25
= 40 + 0.75
Q3 = 40.75 minutes