1. **State the problem:** We are given a set of numbers representing the number of new businesses: 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50. We need to find: - (a) The median number of new businesses. - (b) The largest number of new businesses. - (c) The third quartile (Q\_3) of the numbers of new businesses. 2. **Recall definitions and formulas:** - The **median** is the middle value when the data is ordered. - The **largest number** is the maximum value in the data set. - The **third quartile (Q\_3)** is the median of the upper half of the data (above the median). 3. **Order the data:** The data is already ordered: $$0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50$$ 4. **Find the median:** - There are 11 data points (odd number). - Median is the value at position $\frac{11+1}{2} = 6$. - The 6th value is $25$. 5. **Find the largest number:** - The largest number is the last value in the ordered list: $50$. 6. **Find the third quartile (Q\_3):** - The median splits the data into two halves: - Lower half (below median): $0, 5, 10, 15, 20$ - Upper half (above median): $30, 35, 40, 45, 50$ - Find the median of the upper half (5 values): - Position $\frac{5+1}{2} = 3$ in the upper half. - The 3rd value in upper half is $40$. **Final answers:** - (a) Median = $25$ - (b) Largest number = $50$ - (c) Third quartile (Q\_3) = $40$