Given the numbers:
456, 503, 375, 500, 675, 1350, 120, 375, 500, 450, 620.
To solve this question, let's divide it into sessions A, B, and C.
Session A: Determining the 5 number summary.
The 5 number summary consists in:
1. Minimum value
2. First Quartile (Q1)
3. Median
4. Third Quartile (Q3)
5. Maximum value
Step 01: Find the outliers.
To determine the 5 number summary, you have to remove the outliers.
The numbers 120 and 1350 are very different from the other numbers and thus are the outliers.
Now, use the set of data: 456, 503, 375, 500, 675, 375, 500, 450, 620.
Step 02: Write the numbers in ascending order.
375, 375, 450, 456, 500, 500, 503, 620, 675.
Step 03: Find the minimum value.
The minimum value is the first value in the list.
Minimum = 375.
Step 04: Find the median.
From a set of 9 numbers, the median is the number in the 5th position.
Median = 500.
Step 05: Find the maximum.
The maximum value is the last value in the list.
Maximum = 675.
Step 06: Find Q1.
Q1 is the median (the middle) of the lower half of the data. So, is the median of 375, 375, 450, 456.
Since there are 4 numbers, Q1 is the mean of terms 2 and 3:
Q1 = (375+450)/2
Q1 = 412.5
Step 07: Find Q3.
Q3 is the median of the upper half of the data. So, is the median of 500, 503, 620, 675.
Q3 = (503 + 620)/2
Q3 = 561.5
So, the 5 number summary is:
Minimum = 375.
Q1 = 412.5
Median = 500.
Q3 = 561.5
Maximum = 675.
Session B: Determining the outliers.
As shown in session B, the outliers are 120 and 1350.
Session C: Draw the box and whisker plot.
The box and whisker plot with the 5 number summary is presented below.