Question

weight away, a company that sells weight-loss plans, often advertises the effectiveness of its plans by highlighting the stories of a few clients who have lost extraordinary amounts of weight. the following histogram gives information about more \typical\ clients, summarizing the weight loss (in pounds) over the past month for a sample of 50 clients. (note that a negative value for weight loss represents a weight gain.) based on the histogram, draw the ogive (the cumulative frequency polygon) for the weight away data.

Explanation:

Step1: Calculate cumulative frequencies

• For -10: Cumulative frequency = 6
• For 0: Cumulative frequency = 6 + 7 = 13
• For 10: Cumulative frequency = 13 + 12 = 25
• For 20: Cumulative frequency = 25 + 10 = 35
• For 30: Cumulative frequency = 35 + 9 = 44
• For 40: Cumulative frequency = 44 + 6 = 50
• For 50: Cumulative frequency = 50 (or 0, but as a closed ogive, start at 0 before -10: cumulative frequency 0 at -10 left, then 6 at -10, 13 at 0, 25 at 10, 35 at 20, 44 at 30, 50 at 40, and 50 at 50 (or close at 50 with 50)).

Step2: Plot points

• Plot ( -10, 0 ) [starting point], ( -10, 6 ), ( 0, 13 ), ( 10, 25 ), ( 20, 35 ), ( 30, 44 ), ( 40, 50 ), ( 50, 50 ) [ending point]. Connect these points with straight lines to form the ogive.

Answer:

To draw the ogive:

1. Calculate cumulative frequencies:

• Before -10: \( 0 \)
• At -10: \( 6 \)
• At 0: \( 6 + 7 = 13 \)
• At 10: \( 13 + 12 = 25 \)
• At 20: \( 25 + 10 = 35 \)
• At 30: \( 35 + 9 = 44 \)
• At 40: \( 44 + 6 = 50 \)
• At 50: \( 50 \)

1. Plot points on the cumulative frequency graph:

\( (-10, 0) \), \( (-10, 6) \), \( (0, 13) \), \( (10, 25) \), \( (20, 35) \), \( (30, 44) \), \( (40, 50) \), \( (50, 50) \).

1. Connect points with straight lines to form the cumulative frequency polygon (ogive).