Kobe asked a question and recorded the answers in the table below. Is there variability in the answers?
Hours Each Student Watched TV on Saturday
2, 2, 3, 4, 5, 1, 0, 0, 4, 5, 8, 9, 8, 4, 4, 3, 2, 2, 1, 3, 0
Yes, there is variability in the answers. The range of hours of TV watched on Saturday is from 0 to 9, indicating a wide range of answers. Additionally, there are multiple different values recorded in the table, indicating that not all students watched the same amount of TV.
To determine whether there is variability in the answers, we need to calculate the range and the standard deviation of the data set.
1. Range:
The range is the difference between the maximum and minimum values in the data set.
In this case, the maximum value is 9 and the minimum value is 0.
Range = 9 - 0 = 9.
2. Standard Deviation:
The standard deviation measures how spread out the values are from the mean. A higher standard deviation indicates more variability in the data.
To calculate the standard deviation, we need to follow these steps:
Step 1: Find the mean of the data set.
To find the mean, add up all the numbers and divide by the total count.
Mean = (2 + 2 + 3 + 4 + 5 + 1 + 0 + 0 + 4 + 5 + 8 + 9 + 8 + 4 + 4 + 3 + 2 + 2 + 1 + 3 + 0) / 21
Mean = 77 / 21
Mean ≈ 3.67 (rounded to two decimal places).
Step 2: Find the difference between each value and the mean, squared.
(2 - 3.67)^2 = 2.57
(2 - 3.67)^2 = 2.57
(3 - 3.67)^2 = 0.45
(4 - 3.67)^2 = 0.11
(5 - 3.67)^2 = 2.25
(1 - 3.67)^2 = 7.78
(0 - 3.67)^2 = 13.42
(0 - 3.67)^2 = 13.42
(4 - 3.67)^2 = 0.11
(5 - 3.67)^2 = 2.25
(8 - 3.67)^2 = 18.22
(9 - 3.67)^2 = 28.11
(8 - 3.67)^2 = 18.22
(4 - 3.67)^2 = 0.11
(4 - 3.67)^2 = 0.11
(3 - 3.67)^2 = 0.45
(2 - 3.67)^2 = 2.57
(2 - 3.67)^2 = 2.57
(1 - 3.67)^2 = 7.78
(3 - 3.67)^2 = 0.45
(0 - 3.67)^2 = 13.42
Step 3: Find the average of the squared differences.
Average = (2.57 + 2.57 + 0.45 + 0.11 + 2.25 + 7.78 + 13.42 + 13.42 + 0.11 + 2.25 + 18.22 + 28.11 + 18.22 + 0.11 + 0.11 + 0.45 + 2.57 + 2.57 + 7.78 + 0.45 + 13.42) / 21
Average ≈ 6.10 (rounded to two decimal places).
Step 4: Take the square root of the average.
Standard Deviation = √6.10
Standard Deviation ≈ 2.47 (rounded to two decimal places).
Conclusion:
Based on the calculations, there is variability in the answers as indicated by the range (9) and the standard deviation (2.47).
You have a job that pays $15.00 for each day you show up, plus $8.50 per hour. Which expression shows the amount you make in one day if you work for h hours?
The expression that shows the amount you make in one day if you work for h hours is:
$15.00 + ($8.50/h) * h
Brittany paid a total of $36.00 for 3 pairs of pants. If each pair of pants costs the same amount, what is the price of one pair of pants?
To find the price of one pair of pants, we can divide the total cost by the number of pairs of pants.
Price of one pair of pants = Total cost / Number of pairs of pants
Price of one pair of pants = $36.00 / 3 pairs of pants
Price of one pair of pants = $12.00
Therefore, the price of one pair of pants is $12.00.
All of the values in the set of data fall between 60 and
50
60
70
80
90
100
There seems to be confusion in the range of values mentioned. If all the values in the set of data fall between 60 and 100, then the correct range of values would be:
60, 70, 80, 90, 100
In this case, the lowest value in the data set is 60 and the highest value is 100. Thus, the range is calculated by subtracting the lowest value from the highest value:
Range = 100 - 60 = 40
Therefore, the correct range of values for the given set of data is 40.
Which expression means "10 divided by a number w and then increased by 13"?
The expression that means "10 divided by a number w and then increased by 13" is:
10/w + 13