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.) data table full data set 0 3 1 0 2 1 5 2 0 4 1 0 3 1 0 2 1 4 2 0 3 1 0 3 1 0 2 0 4 2

Explanation:

Step1: Count the frequency for each \(x\)

• For \(x = 0\): Count the number of \(0\)s in the data set. There are \(8\) zeros.
• For \(x = 1\): Count the number of \(1\)s. There are \(7\) ones.
• For \(x = 2\): Count the number of \(2\)s. There are \(6\) twos.
• For \(x = 3\): Count the number of \(3\)s. There are \(5\) threes.
• For \(x = 4\): Count the number of \(4\)s. There are \(3\) fours.
• For \(x = 5\): Count the number of \(5\)s. There is \(1\) five.

Step2: Calculate the relative frequency \(\frac{f}{n}\)

Since \(n=30\) (total number of data points):

• For \(x = 0\): \(\frac{8}{30}\approx 27\%\)
• For \(x = 1\): \(\frac{7}{30}\approx 23\%\)
• For \(x = 2\): \(\frac{6}{30}= 20\%\)
• For \(x = 3\): \(\frac{5}{30}\approx 17\%\)
• For \(x = 4\): \(\frac{3}{30}= 10\%\)
• For \(x = 5\): \(\frac{1}{30}\approx 3\%\)

Answer:

Number \(x\)	Frequency \(f\)	Relative Frequency \(\frac{f}{n}\)
\(1\)	\(7\)	\(23\%\)
\(2\)	\(6\)	\(20\%\)
\(3\)	\(5\)	\(17\%\)
\(4\)	\(3\)	\(10\%\)
\(5\)	\(1\)	\(3\%\)