Check my answers please!
Thanks a lot.
Five students reported that the previous night they slept: 7,8,7,10,9 hours.
Calculate the sample varience and standard deviation.
sample varience = 1346.5
standard deviation = 36.7
Consider this. Ths standard deviation can never be larger than the range of scores. Assuming that you are still talking in hours, you answer is much larger.
mean = 8.2
Differences obtained by subtracting the score from the mean =
1.2
.2
1.2
-1.8
-.8
Squaring each of these gives you
1.44
.04
1.44
3.24
.64
Totaling 6.8. Dividing this by N (5) gives you 1.36 = variance
The square root of the variance is the standard deviation.
I hope this helps. Thanks for asking.
Let's go through the steps to verify the answers for the sample variance and standard deviation calculations.
To calculate the sample variance, follow these steps:
1. Find the mean (average) of the data set.
Sum all the values: 7 + 8 + 7 + 10 + 9 = 41
Divide the sum by the number of values: 41 / 5 = 8.2 (mean)
2. Subtract the mean from each data point and square the result.
For example, for the first data point, 7 - 8.2 = -1.2, then (-1.2)^2 = 1.44
Repeat this for all data points:
1.2, 0.04, 1.44, 3.24, 0.64
3. Sum all the squared differences from step 2.
1.44 + 0.04 + 1.44 + 3.24 + 0.64 = 6.8
4. Divide the sum from step 3 by the number of data points (sample size).
6.8 / 5 = 1.36 (sample variance)
Now, let's calculate the standard deviation:
5. Take the square root of the sample variance from step 4.
√1.36 = 1.166 (approx. standard deviation)
Comparing this result to the given answer, we see that the sample variance is indeed 1.36, not 1346.5, and the standard deviation is 1.166, not 36.7. The original answers provided are incorrect.
Therefore, the correct answers are:
Sample variance: 1.36
Standard deviation: 1.166
Note: It's important to be cautious while calculating and interpreting statistics to avoid errors.