(a) Draw a cumulative frequency graph with the given cumulative frequencies at the upper class boundaries: (200, 16), (300, 46), (500, 88), (900, 122), (1200, 134), (1600, 140).

(b) To find the interquartile range (IQR), use the cumulative frequency graph:

• Lower quartile (LQ) at 25% of 140: 35
• Upper quartile (UQ) at 75% of 140: 105
• IQR = UQ - LQ = 105 - 35 = 70

(c) Calculate the mean and standard deviation:

• Class midpoints: 100, 250, 400, 700, 1050, 1400
• Frequencies: 16, 30, 42, 34, 12, 6
• Mean: \(\frac{16 \times 100 + 30 \times 250 + 42 \times 400 + 34 \times 700 + 12 \times 1050 + 6 \times 1400}{140} = 505\)
• Variance: \(\frac{16 \times 100^2 + 30 \times 250^2 + 42 \times 400^2 + 34 \times 700^2 + 12 \times 1050^2 + 6 \times 1400^2}{140} - 505^2 = 324^2\)
• Standard deviation: \(\sqrt{324^2} = 324\)