how do you find the five figure summary of this frequency table?

Question

x	f
2	3
3	2
4	2
5	3
6	4
7	2
8	3
9	2

total:21

Answer 1

The minimum x value is 2; the maximum is 9. These are two if the required statistics. We need the median which is the central value of the 21 ordered data values. This is the 11th element, which is 6. The median is also the 2nd quartile Q2, the third required statistic.

The remaining two are Q1 and Q3. These are the medians of the size 10 groups on either side of Q2. The median of 10 elements is the average of the 5th and 6th elements. So for Q1 this would be the average of 3 and 4, 3.5. Q1=3.5.

For Q3=average of 7 and 8=7.5.

SUMMARY: Min=2, Max=9, Median (Q2)=6, Q1=3.5, Q3=7.5 (IQR=7.5-3.5=4).

By laying out the data in a line it's easier to see:

2

2

2

3

3

4

4

5

5

5

Q2=6

6

6

6

7

7

8

8

8

9

9