What is the standard deviation of the data set? 1, 4, 2, 2, 8, 7, 3 Round your answer to the nearest tenth.
1 answer:
Standard deviation is a measurement of a collection of values' variance or dispersion. The standard deviation of the data set is 2.474.
<h3>How to calculate the standard deviation of a data set?</h3>Step 1: Find the mean
Step 2: Find each score’s deviation from the mean
Step 3: Square each deviation from the mean
Step 4: Find the sum of squares
Step 5: Apply the formula
The data set that is given to us is {1, 4, 2, 2, 8, 7, 3}, now use the steps to calculate the standard deviation.
Step 1: Find the mean
The mean of the given data set can be written as,
Step 2: Find each score’s deviation from the mean
1 - 3.857 = -2.857
4 - 3.857 = 0.143
2 - 3.857= -1.857
2 - 3.857= -1.857
8 - 3.857 = 4.143
7 - 3.857 = 3.143
3 - 3.857 = -0.857
Step 3: Square each deviation from the mean
-2.857² = 8.162
0.143² = 0.02
-1.857² = 3.447
-1.857² = 3.447
4.143² = 17.165
3.143² = 9.877
-0.857²= 0.735
Step 4: Find the sum of squares
8.162+0.20+3.447+3.447+17.165+9.877+0.735 = 42.857
Step 5: Apply the formula
Hence, the standard deviation of the data set is 2.474.
Learn more about Standard Deviation:
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Answer:
Now we can calculate the degrees of freedom for the statistic given by:
And we can calculate the p value given by:
And we can find the p value using the following excel code:
"=1-CHISQ.DIST(19.221,2,TRUE)"
Since the p values is higher than a significance level for example , we can reject the null hypothesis at 5% of significance, and we can conclude that the two variables are dependent at 5% of significance.
Step-by-step explanation:
Previous concepts
A chi-square goodness of fit test "determines if a sample data matches a population".
A chi-square test for independence "compares two variables in a contingency table to see if they are related. In a more general sense, it tests to see whether distributions of categorical variables differ from each another".
Solution to the problem
Assume the following dataset:
Size Company/ Heal. Ins. Yes No Total
Small 32 18 50
Medium 68 7 75
Large 89 11 100
_____________________________________
Total 189 36 225
We need to conduct a chi square test in order to check the following hypothesis:
H0: independence between heath insurance coverage and size of the company
H1: NO independence between heath insurance coverage and size of the company
The statistic to check the hypothesis is given by:
The table given represent the observed values, we just need to calculate the expected values with the following formula
And the calculations are given by:
And the expected values are given by:
Size Company/ Heal. Ins. Yes No Total
Small 42 8 50
Medium 63 12 75
Large 84 16 100
_____________________________________
Total 189 36 225
And now we can calculate the statistic:
Now we can calculate the degrees of freedom for the statistic given by:
And we can calculate the p value given by:
And we can find the p value using the following excel code:
"=1-CHISQ.DIST(19.221,2,TRUE)"
Since the p values is higher than a significance level for example , we can reject the null hypothesis at 5% of significance, and we can conclude that the two variables are dependent at 5% of significance.