question 1 (1 point)\nhere is a data set:\n1 2 3 3 4 4 4 4\n5 5 6 7\n1. what happens to the mean and…

question 1 (1 point)\nhere is a data set:\n1 2 3 3 4 4 4 4\n5 5 6 7\n1. what happens to the mean and standard deviation of the data set when the 7 is changed to a 70?\nthe mean increases from ______ to ______ and the standard deviation ______ (decreases, increases) from about 1.58 to ______\n2. for the data set with the value of 70, why would the median be a better choice for the measure of center than the mean?\nthe median would be a better choice because the data set with the 70 is a ______ (bell - shaped, uniform, skewed) distribution.\nblank 1:\nblank 2:\nblank 3:\nblank 4:\nblank 5:

question 1 (1 point)\nhere is a data set:\n1 2 3 3 4 4 4 4\n5 5 6 7\n1. what happens to the mean and standard deviation of the data set when the 7 is changed to a 70?\nthe mean increases from ______ to ______ and the standard deviation ______ (decreases, increases) from about 1.58 to ______\n2. for the data set with the value of 70, why would the median be a better choice for the measure of center than the mean?\nthe median would be a better choice because the data set with the 70 is a ______ (bell - shaped, uniform, skewed) distribution.\nblank 1:\nblank 2:\nblank 3:\nblank 4:\nblank 5:

Answer

Explanation:

Step1: Calculate original mean

The original data set is (1,2,3,3,4,4,4,4,5,5,6,7). The sum of the data is (1 + 2+3+3 + 4+4+4+4+5+5+6+7=48), and there are (n = 12) data - points. The original mean (\bar{x}_1=\frac{48}{12}=4).

Step2: Calculate new mean

When (7) is changed to (70), the new sum is (48 - 7+70=111). The new mean (\bar{x}_2=\frac{111}{12}=9.25).

Step3: Analyze standard - deviation change

The standard deviation measures the spread of the data. When a value is changed from (7) to (70), the data becomes more spread out. So the standard deviation increases. To calculate the new standard deviation, we use the formula (s=\sqrt{\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}}). For the new data set, first calculate (\sum_{i = 1}^{12}(x_i - 9.25)^2). After calculation, the new standard deviation is approximately (18.97).

Step4: Analyze measure of center

The original data set is relatively symmetric. But when (7) is changed to (70), the data set is skewed because of the out - lier (70). In a skewed distribution, the median is a better measure of the center than the mean as the mean is affected by extreme values.

Answer:

Blank 1: (4) Blank 2: (9.25) Blank 3: increases Blank 4: (18.97) Blank 5: skewed