Question

this list shows how many hours twenty batteries lasted when they ran continually in a flashlight. 78 31 47 51 16 58 60 10 30 40 46 63 65 10 93 22 13 47 64 93 what is the best frequency table for the battery life data? a. battery life hours tally frequency 0 - 10 || 2 20 - 30 || 2 40 - 50 |||| 4 60 - 70 || 2 80 - 90 || 2 b. battery life hours tally frequency 0 - 24 |||| 5 25 - 49 |||| 5 50 - 74 |||| 6 75 - 99 |||| 4 c. battery life hours tally frequency 0 - 19 |||| 4 20 - 39 |||| 3 40 - 59 |||| 6 60 - 79 |||| 5 80 - 99 |||| 2 d. battery life hours tally frequency 0 - 20 |||| 4 20 - 40 |||| 4 40 - 60 |||| 7 60 - 80 |||| 5

Explanation:

Step1: Count data in each range for option a

For \(0 - 10\): 2 values (\(10,10\)); for \(20 - 30\): 2 values (\(31,30\)); for \(40 - 50\): 4 values (\(47,51,40,46\)); for \(60 - 70\): 2 values (\(60,63\)); for \(80 - 90\): 2 values (\(93,93\)). But there are values like \(16,13,22\) not accounted for in \(0 - 10\) range properly.

Step2: Count data in each range for option b

For \(0 - 24\): 5 values (\(16,10,10,22,13\)); for \(25 - 49\): 5 values (\(31,47,40,46,47\)); for \(50 - 74\): 6 values (\(51,58,60,63,65,64\)); for \(75 - 99\): 4 values (\(78,93,93\)). This seems to group the data in a more appropriate way.

Step3: Count data in each range for option c

For \(0 - 19\): 4 values (\(16,10,10,13\)); for \(20 - 39\): 3 values (\(31,30,22\)); for \(40 - 59\): 6 values (\(47,51,40,46,58,60\)); for \(60 - 79\): 5 values (\(63,65,64,78\)); for \(80 - 99\): 2 values (\(93,93\)). The groupings are a bit odd - for example, \(40 - 59\) combines two - digit numbers in a less intuitive way.

Step4: Count data in each range for option d

For \(0 - 20\): 4 values (\(16,10,10,13\)); for \(20 - 40\): 4 values (\(31,30,22\)); for \(40 - 60\): 7 values (\(47,51,40,46,58,60\)); for \(60 - 80\): 5 values (\(63,65,64,78\)). Similar to option c, the groupings are not as well - defined as option b.

Answer:

B. Battery Life

Hours	Tally	Frequency
\(25 - 49\)	5	5
\(50 - 74\)	6	6
\(75 - 99\)	4	4