Mathematics 10 — Exercise 11.1 · Q4

Full question

Find Q1,Q3,median,range,IQR and extremes. Draw a box-and-whisker plot. Data: 102, 98, 95, 100, 93, 110, 108, 104, 97, 96, 92, 101, 99, 105, 107

Step-by-step solution

1. Arrange ALL observations in increasing order, keeping repeated values.

   $$(92,93,95,96,97,98,99,100,101,102,104,105,107,108,110)$$

2. Q1 position: (n+1)×1/4. Positions are counted from 1.

   $$15+1\times \frac{1}{4}=4$$

3. Read observation 4.

   $$96$$

4. Median position: (n+1)×1/2. Positions are counted from 1.

   $$15+1\times \frac{1}{2}=8$$

5. Read observation 8.

   $$100$$

6. Q3 position: (n+1)×3/4. Positions are counted from 1.

   $$15+1\times \frac{3}{4}=12$$

7. Read observation 12.

   $$105$$

8. Range: subtract the lower value from the upper.

   $$110-92$$

9. Calculate this operation before combining the remaining terms.

   $$110-92=18$$

10. IQR: subtract the lower value from the upper.

    $$105-96$$

11. Calculate this operation before combining the remaining terms.

    $$105-96=9$$

12. Mark minimum, Q1, median, Q3 and maximum on a common number line. Draw a box from Q1 to Q3, a median line, and whiskers to the extremes.

Answer

Q1=96; median=100; Q3=105; range=18; IQR=9; min=92; max=110