Find the mean, variance, and standard deviation for the following data set:
49, 32, 35, 43, 45, 40, 53, 55, 42
Question 1
What is being asked in the problem and what does that mean? What plan am I going to try? (1 sentence)
Question 2
I will write out my response to the question, explaining my answer and what it means. (1 sentence)
(solve step by step at the end)
Question 1: The problem is asking for the mean, variance, and standard deviation of the given data set. I will calculate these statistical measures to describe the central tendency and dispersion of the data set.
Question 2: I will calculate the mean, variance, and standard deviation of the data set 49, 32, 35, 43, 45, 40, 53, 55, 42, to find the average, spread, and variability of the values.
Step by step solution:
Mean:
(49 + 32 + 35 + 43 + 45 + 40 + 53 + 55 + 42) / 9 = 399 / 9 = 44.33
Variance:
1. Find the squared difference between each value and the mean:
(49-44.33)^2 + (32-44.33)^2 + (35-44.33)^2 + (43-44.33)^2 + (45-44.33)^2 + (40-44.33)^2 + (53-44.33)^2 + (55-44.33)^2 + (42-44.33)^2 = 1179.33
2. Divide the sum by the number of values (9):
1179.33 / 9 = 131.03
Standard Deviation:
√131.03 = 11.45
Therefore, the mean of the data set is 44.33, the variance is 131.03, and the standard deviation is 11.45.
can you double check your answers?
I got Mean 43.78
Variance 61.22
Standard Deviation 7.82
Let me know if I'm wrong
I made an error in my calculations. Let's double-check the mean, variance, and standard deviation of the data set:
Mean:
(49 + 32 + 35 + 43 + 45 + 40 + 53 + 55 + 42) / 9 = 394 / 9 = 43.78
Variance:
1. Find the squared difference between each value and the mean:
(49-43.78)^2 + (32-43.78)^2 + (35-43.78)^2 + (43-43.78)^2 + (45-43.78)^2 + (40-43.78)^2 + (53-43.78)^2 + (55-43.78)^2 + (42-43.78)^2 = 491.11
2. Divide the sum by the number of values (9):
491.11 / 9 = 54.57
Standard Deviation:
√54.57 = 7.39
After double-checking, the correct values are:
Mean: 43.78
Variance: 54.57
Standard Deviation: 7.39
You were close, but the correct variance should be 54.57 and the correct standard deviation should be 7.39.