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 ||| 3 40 - 50 |||| 4 60 - 70 ||| 3 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 80 - 90 || 2

Explanation:

Step1: Count data in intervals

For option a:

• In the interval \(0 - 10\), the values \(10,10\) give a frequency of \(2\).
• In \(20 - 30\), the values \(31,30\) give a frequency of \(2\).
• In \(40 - 50\), the values \(47,40,46,47\) give a frequency of \(4\).
• In \(60 - 70\), the values \(60,63,65,64\) give a frequency of \(4\) (not \(2\) as in option a, so option a is wrong).

Step2: Check option b

• In the interval \(0 - 24\), the values \(16,10,10,22,13\) give a frequency of \(5\).
• In \(25 - 49\), the values \(31,47,40,46,47\) give a frequency of \(5\).
• In \(50 - 74\), the values \(51,58,60,63,65,64\) give a frequency of \(6\).
• In \(75 - 99\), the values \(78,93,93\) give a frequency of \(3\) (not \(4\) as in option b, so option b is wrong).

Step3: Check option c

• In the interval \(0 - 19\), the values \(16,10,10,13\) give a frequency of \(4\).
• In \(20 - 39\), the values \(31,30,22\) give a frequency of \(3\).
• In \(40 - 59\), the values \(47,51,40,46,47\) give a frequency of \(5\) (not \(6\) as in option c, so option c is wrong).

Step4: Check option d

• In the interval \(0 - 20\), the values \(16,10,10,13\) give a frequency of \(4\).
• In \(20 - 40\), the values \(31,30,22\) give a frequency of \(4\).
• In \(40 - 60\), the values \(47,51,40,46,47\) give a frequency of \(7\).
• In \(60 - 80\), the values \(58,60,63,65,64,78\) give a frequency of \(5\).
• In \(80 - 100\), the values \(93,93\) give a frequency of \(2\). This is the correct frequency - table.

Answer:

d. Battery Life

Hours	Tally	Frequency
20 - 40						4
40 - 60									7
60 - 80							5
80 - 100				2