Question

In Applied Life Data Analysis (Wiley, 1982), Wayne Nelson presents the breakdown time of an insulating fluid between electrodes at 34 kV. The times, in minutes, are as follows: 0.13, 0.68, 0.91, 1.36, 2.74, 3.08, 4.07, 4.71, 4.96, 6.56, 7.29, 7.91, 8.37, 12.11, 31.61, 32.65, 33.78, 36.72, and 72.96. Calculate the sample mean and sample standard deviation. Round the answers to 3 decimal places.

Answer 1

Answer:

Mean  = 14.347 and Standard Deviation = 18.89

Step-by-step explanation:

Mean = Sum of all the numbers/total numbers = 272.6/19 = 14.347

For standard deviation, at first we will find variance which is

variance = The sum of the squared differences between each data point and the mean, divided by the number of data points (n) - 1:

x= data points

n= total number of data points

= ∑(x_i - Mean (x))^2/(n-1)

variance = 357

Standard deviation = $\sqrt{variance}$

SD = $\sqrt{357}$

SD = 18.89

Answer 2

Answer:

The mean= 14.347

The standard deviation =18.390

Step-by-step explanation:

The mean or average of a set of scores = the summation of the set of scores divided by the summation of the frequency of the respective scores.

Adding up the scores we have:

0.13+0.68+0.91+1.36+2.74+3.08+4.07+4.71+4.96+6.56+7.29+7.91+8.37+12.11+31.61+32.65+33.78+36.72+72.96 = 272.60

The frequency or number of scores is 19, so dividing this figure by the number of items in the set, we have:

272/19 =14.347

Therefore the mean of the scores (time, in minutes) is 14.347(to 3 decimal places)

In order to calculate the standard deviation of the set, we need to find the summation of the squares of the different deviations from the mean.

Example, 0.13 is the first score in the data. We subtract the mean (14.35) from 0.13 and we'll have 14.22 which is the score's deviation from the mean. the next step is to find the square of the deviation,14.22 which will be 202.208.

We'll repeat this same process for the remainder of the scores and then sum up the squares of the deviations.Doing this, the summation of the squares of all the deviations from the mean score will be = 6425.67

Once this is calculated we then solve to obtain the standard deviation of the scores by applying the formula:

√summation of (x - mean deviations)/total number of scores

=√(6425.67/19)

= √ (338.193)

= 18.390( to 3 decimal places)

Therefore the mean and the standard deviation of the set of scores are 14.347 and 18.390 respectively