Question

a magazine identified the following five \maintenance\ activities often performed by people as summer approaches: 1. prep the car for road trips; 2. clean up the house or apartment; 3. groom the garden; 4. exercise the body; 5. organize the wardrobe. the following data are the responses of 30 people who were asked, on june 1st, how many of the five they had accomplished. complete parts (a) through (c) below.
click the icon to view the data.
(a) construct frequency and relative frequency distributions.
(round to the nearest integer as needed.)

number ( x ) frequency ( f ) relative frequency ( \frac{f}{n} )
0
1 7
2 5
3 3
4 2
5 1

Explanation:

Step1: Calculate the frequency for \(x = 0\)

We know that the total number of people \(n=30\).
The sum of the given frequencies \(7 + 5+3 + 2+1=18\).
So the frequency \(f\) for \(x = 0\) is \(n-(7 + 5+3 + 2+1)=30 - 18=12\).

Step2: Calculate the relative frequencies

The formula for relative frequency is \(\frac{f}{n}\times100\%\).

• For \(x = 0\): \(\frac{12}{30}\times100\% = 40\%\)
• For \(x = 1\): \(\frac{7}{30}\times100\%\approx23\%\)
• For \(x = 2\): \(\frac{5}{30}\times100\%\approx17\%\)
• For \(x = 3\): \(\frac{3}{30}\times100\% = 10\%\)
• For \(x = 4\): \(\frac{2}{30}\times100\%\approx7\%\)
• For \(x = 5\): \(\frac{1}{30}\times100\%\approx3\%\)

Answer:

Number \(x\)	Frequency \(f\)	Relative Frequency \(\frac{f}{n}\)
\(1\)	\(7\)	\(23\%\)
\(2\)	\(5\)	\(17\%\)
\(3\)	\(3\)	\(10\%\)
\(4\)	\(2\)	\(7\%\)
\(5\)	\(1\)	\(3\%\)