Question

question 2
this data is from a sample. calculate the mean, standard deviation, and variance.

x

21.2

34.9

45.6

15.6

20.8

49.7

14.3

please show the following answers to 2 decimal places.
sample mean = 28.87
sample standard deviation = 14.51
sample variance =
ooops - now you discover that the data was actually from a population! so now you must give the population standard deviation.
population standard deviation =

Explanation:

Step1: Calculate sample mean

Sum data: 21.2+34.9+45.6+15.6+20.8+49.7+14.3=202.1
Mean: \( \frac{202.1}{7} \approx 28.87 \)

Step2: Calculate squared differences from mean

\( (21.2-28.87)^2=58.83 \), \( (34.9-28.87)^2=36.36 \), \( (45.6-28.87)^2=279.89 \), \( (15.6-28.87)^2=176.09 \), \( (20.8-28.87)^2=65.12 \), \( (49.7-28.87)^2=433.89 \), \( (14.3-28.87)^2=212.28 \)
Sum: \( 58.83+36.36+279.89+176.09+65.12+433.89+212.28=1262.46 \)

Step3: Sample variance

\( \frac{1262.46}{7-1} \approx 210.41 \)

Step4: Sample standard deviation

\( \sqrt{210.41} \approx 14.51 \)

Step5: Population standard deviation

\( \sqrt{\frac{1262.46}{7}} \approx 13.43 \)

Answer:

Sample Mean = 28.87
Sample Standard Deviation = 14.51
Sample Variance = 210.41
Population Standard Deviation = 13.43