Question

a national survey asked people, \how often do you eat out for dinner, instead of at home?\ the frequencies were as follows. complete parts (a) through (d)

response	frequency
once or twice a week	510
a few times a month	970
very rarely	390
never	43

(a) construct a relative frequency distribution of the data

response	relative frequency
once or twice a week
a few times a month
very rarely
never

(round to three decimal places as needed.)

Explanation:

Step1: Calculate the total frequency

First, we need to find the sum of all the frequencies. The frequencies are 358, 510, 970, 390, and 43. So, the total frequency \( N \) is:
\( N = 358 + 510 + 970 + 390 + 43 \)
\( N = 358 + 510 = 868 \); \( 868 + 970 = 1838 \); \( 1838 + 390 = 2228 \); \( 2228 + 43 = 2271 \)

Step2: Calculate relative frequency for each response

The relative frequency of a response is calculated as \( \text{Relative Frequency} = \frac{\text{Frequency of the response}}{\text{Total Frequency}} \)

• For "Several times a week": \( \frac{358}{2271} \approx 0.1576 \approx 0.158 \) (rounded to three decimal places)
• For "Once or twice a week": \( \frac{510}{2271} \approx 0.2246 \approx 0.225 \) (rounded to three decimal places)
• For "A few times a month": \( \frac{970}{2271} \approx 0.4271 \approx 0.427 \) (rounded to three decimal places)
• For "Very rarely": \( \frac{390}{2271} \approx 0.1717 \approx 0.172 \) (rounded to three decimal places)
• For "Never": \( \frac{43}{2271} \approx 0.0189 \approx 0.019 \) (rounded to three decimal places)

Answer:

Response	Relative Frequency
Once or twice a week	0.225
A few times a month	0.427
Very rarely	0.172
Never	0.019