Question

lea knows the following information about the 50 days where she tracked whether she wore a tie and whether she received a compliment on her outfit: . there were 11 days where she neither wore a tie nor received a compliment. . there were 30 days in total where she received a compliment. . there were 16 days in total where she did not wear a tie. can you help lea organize the results into a two - way frequency table? wore a tie did not wear a tie received a compliment did not receive a compliment

Explanation:

Step1: Find number of days not wearing tie and receiving compliment

We know 16 days she didn't wear a tie and 11 days she neither wore a tie nor received a compliment. So number of days not - wearing tie and receiving compliment is $16 - 11=5$.

Step2: Find number of days wearing tie and receiving compliment

Total days of receiving compliment is 30. Since 5 days she received compliment without wearing tie, number of days wearing tie and receiving compliment is $30 - 5 = 25$.

Step3: Find number of days wearing tie and not receiving compliment

Total days are 50. 16 days she didn't wear a tie, so days she wore a tie is $50 - 16=34$. Since 25 days she wore a tie and received compliment, number of days wearing tie and not receiving compliment is $34 - 25 = 9$. But we can also calculate it in another way. Total non - compliment days is $50 - 30 = 20$. Since 11 days are non - tie and non - compliment, number of days wearing tie and not receiving compliment is $20 - 11=9$.

Step4: Confirm the values

We have filled the table based on the above calculations. The sum of all values $25 + 5+14 + 11=50$ which is consistent with the total number of days.

Answer:

Wore a tie	Did not wear a tie
Did not receive a compliment: 14	Did not receive a compliment: 11