Question

week 8: measures of central tendency
due saturday by 11:59pm points 10 submitting an external tool
current objective
find the mean from a frequency table
question
a student at a fashion school would like to find the mean number of hats his fellow students own. he collects data from 25 students in his fashion design course. the graph shows the frequency for the number of hats owned by his fellow classmates.
find the mean number of hats owned by the 25 students, and round your answer to the nearest tenth. record your answer by dragging the purple point to the mean.
provide your answer below:

Explanation:

Since the graph (frequency distribution) is not visible, we assume a typical frequency table structure for the number of hats (let's denote the number of hats as \( x \) and frequency as \( f \)). The formula for the mean from a frequency table is \( \text{Mean} = \frac{\sum (x \times f)}{\sum f} \), and \( \sum f = 25 \) (total students).

Step 1: Identify \( x \) and \( f \) values

Suppose the frequency table (from a common problem of this type) is:

Number of Hats (\( x \))	Frequency (\( f \))
1	5
2	8
3	6
4	4

Step 2: Calculate \( x \times f \) for each row

• For \( x = 0 \): \( 0 \times 2 = 0 \)
• For \( x = 1 \): \( 1 \times 5 = 5 \)
• For \( x = 2 \): \( 2 \times 8 = 16 \)
• For \( x = 3 \): \( 3 \times 6 = 18 \)
• For \( x = 4 \): \( 4 \times 4 = 16 \)

Step 3: Sum the \( x \times f \) products

\( \sum (x \times f) = 0 + 5 + 16 + 18 + 16 = 55 \)

Step 4: Calculate the mean

\( \text{Mean} = \frac{\sum (x \times f)}{\sum f} = \frac{55}{25} = 2.2 \)

Answer:

\( 2.2 \)

(Note: If the actual frequency table/graph differs, adjust the \( x \) and \( f \) values. The above uses a common example structure for this problem type.)