Please check my responses! ASAP
Consider the following data set: 3,4,6,7,9,9,11
If 5 were added to each of the values, how would that affect the median?
My Answer: The median would change and increase.
Consider the following data set: 3,4,6,7,9,9,11
If 5 were added to each of the values, how would that affect the standard deviation?
Me: The deviation would increase
Consider the following data set: 3,4,6,7,9,9,11
If 5 were added to each of the values, how would that affect the mean?
Me: The mean would increase if 5 is ADDED to each of the numbers to the data set. assuming I'm not actually changing the amount of numbers in the set it would mean the only thing changing is the overall value of the set.
Mary measures the weights of five newly-hatched pythons in ounces. John converts Mary's measurments into grams. there are 28.35 grams in an ounce here are Mary's results: Python = 1 2 3 4 5
Mary= 1.13oz 1.02oz 1.23oz 1.06oz 1.16oz
Calculate the mean and sample standard deviation of Mary's measurements using the formula for each.
Me: Assuming I'm calculating Mary's data the standard deviation would be 0.08276 and the mean would be 1.12
mean and median will increase by 5
std will not change. Try it. That's the whole point of the std - it is independent of the actual magnitudes, just their spread.
Your µ and σ look ok, too.
To check your responses, let's go through each question and calculation one by one:
1. Consider the following data set: 3, 4, 6, 7, 9, 9, 11. If 5 were added to each of the values, how would that affect the median?
Your answer: The median would change and increase.
Correct! Adding a constant value to each number in a data set does not change the relative order of the values, but it shifts the entire distribution. As a result, the median would increase by 5 units.
2. Consider the same data set: 3, 4, 6, 7, 9, 9, 11. If 5 were added to each of the values, how would that affect the standard deviation?
Your answer: The deviation would increase.
Correct! Adding a constant value to each number in a data set increases the spread of the data, resulting in a higher standard deviation.
3. Consider the same data set: 3, 4, 6, 7, 9, 9, 11. If 5 were added to each of the values, how would that affect the mean?
Your answer: The mean would increase if 5 is ADDED to each of the numbers in the data set.
Correct! When a constant value is added to each number in a data set, the mean also increases by the same constant value. So, in this case, the mean would increase by 5 units.
4. Mary measures the weights of five newly-hatched pythons in ounces. John converts Mary's measurements into grams. There are 28.35 grams in an ounce. Here are Mary's results: Python 1 = 1.13 oz, Python 2 = 1.02 oz, Python 3 = 1.23 oz, Python 4 = 1.06 oz, Python 5 = 1.16 oz. Calculate the mean and sample standard deviation of Mary's measurements using the formulas for each.
Your answer: Assuming I'm calculating Mary's data, the standard deviation would be 0.08276 and the mean would be 1.12.
I'm sorry, but your calculations are incorrect. Let's calculate them together:
First, let's convert the measurements from ounces to grams:
Python 1: 1.13 oz * 28.35 g/oz = 32.0355 g
Python 2: 1.02 oz * 28.35 g/oz = 28.917 g
Python 3: 1.23 oz * 28.35 g/oz = 34.9005 g
Python 4: 1.06 oz * 28.35 g/oz = 30.111 g
Python 5: 1.16 oz * 28.35 g/oz = 32.994 g
Now, let's calculate the mean (average):
Mean = (32.0355 + 28.917 + 34.9005 + 30.111 + 32.994) g / 5 = 29.9914 g, rounded to 5 decimal places.
Next, let's calculate the sample standard deviation (assuming this is a sample, not a population):
Step 1: Calculate the squared deviations from the mean for each measurement:
(32.0355 - 29.9914)^2 = 4.151181
(28.917 - 29.9914)^2 = 1.152737
(34.9005 - 29.9914)^2 = 24.208835
(30.111 - 29.9914)^2 = 0.014592
(32.994 - 29.9914)^2 = 9.021961
Step 2: Calculate the sum of squared deviations:
4.151181 + 1.152737 + 24.208835 + 0.014592 + 9.021961 = 38.549316
Step 3: Divide the sum of squared deviations by (n-1), where n is the number of measurements (5) to get the variance:
Variance = 38.549316 / (5 - 1) = 9.637329
Step 4: Take the square root of the variance to get the sample standard deviation:
Sample standard deviation = √9.637329 = 3.10575, rounded to 5 decimal places.
Therefore, the mean of Mary's measurements is approximately 29.9914 grams, and the sample standard deviation is approximately 3.10575 grams.