Pet Data Summary D11F7B

1. **State the problem:** We have a frequency table for the number of pets owned by students: | Number of Pets ($x$) | Frequency ($f$) | |---------------------|----------------| | 0 | 9 | | 1 | 12 | | 2 | 5 | | 3 | 3 | | 4 | 1 | We need to find: a) The Interquartile Range (IQR) of the pet data. b) The Five-Number Summary (minimum, Q1, median, Q3, maximum). --- 2. **Calculate total number of data points ($n$):** $$n = 9 + 12 + 5 + 3 + 1 = 30$$ 3. **Create the cumulative frequency table:** | Number of Pets ($x$) | Frequency ($f$) | Cumulative Frequency ($CF$) | |---------------------|----------------|-----------------------------| | 0 | 9 | 9 | | 1 | 12 | 9 + 12 = 21 | | 2 | 5 | 21 + 5 = 26 | | 3 | 3 | 26 + 3 = 29 | | 4 | 1 | 29 + 1 = 30 | --- 4. **Find the positions of quartiles:** - $Q1$ position = $\frac{n+1}{4} = \frac{30+1}{4} = \frac{31}{4} = 7.75$th data point - Median ($Q2$) position = $\frac{n+1}{2} = \frac{31}{2} = 15.5$th data point - $Q3$ position = $3 \times \frac{n+1}{4} = 3 \times 7.75 = 23.25$th data point --- 5. **Locate $Q1$ (7.75th data point):** - The first 9 data points are all 0 (from cumulative frequency). - Since 7.75 $\leq$ 9, $Q1 = 0$ 6. **Locate Median (15.5th data point):** - Cumulative frequency up to 0 pets is 9. - Next 12 data points are 1 pet, covering data points 10 to 21. - Since 15.5 is between 10 and 21, median = 1 7. **Locate $Q3$ (23.25th data point):** - Cumulative frequency up to 1 pet is 21. - Next 5 data points are 2 pets, covering data points 22 to 26. - Since 23.25 is between 22 and 26, $Q3 = 2$ --- 8. **Find minimum and maximum:** - Minimum = smallest number of pets = 0 - Maximum = largest number of pets = 4 --- 9. **Calculate Interquartile Range (IQR):** $$IQR = Q3 - Q1 = 2 - 0 = 2$$ --- 10. **Five-Number Summary:** - Minimum = 0 - $Q1 = 0$ - Median = 1 - $Q3 = 2$ - Maximum = 4 --- **Final answers:** - a) Interquartile Range (IQR) = $2$ - b) Five-Number Summary = $(0, 0, 1, 2, 4)$