I'll do problem 1 to get you started
First sort the values from smallest to largest and you should end up with this set
{1, 6, 7, 11, 13, 16, 18, 21, 22, 23}
The smallest value is 1 and the largest value is 23, so the min and max are 1 and 23 in that order.
We have ten values in this set. The middle-most number is going to be between the 10/2 = 5th slot and the 6th slot. The numbers 13 and 16 are in the fifth and sixth slots respectively. Average those values to get (13+16)/2 = 29/2 = 14.5
The median is 14.5 which is another name for the second quartile (Q2).
Now split the data set into two halves
L = lower half of values smaller than the median
U = upper half of values larger than the median
In this case,
L = {1, 6, 7, 11, 13}
U = {16, 18, 21, 22, 23}
sets L and U have five items each
Find the median of set L and U to get 7 and 21 respectively. These medians of L and U represent the values of Q1 and Q3 in that order.
Q1 = first quartile = 7
Q3 = third quartile = 21
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Answer:
The five number summary for problem 1 is
- Minimum = 1
- Q1 = 7
- Q2 = 14.5 (this is the median)
- Q3 = 21
- Maximum = 23