Compute the mean, range, and standard deviation for the data items in each of the three samples. Then describe one way in which the samples are alike and one way in which they are different.
Sample A. 18, 22, 26, 30, 34, 38, 42 으
Sample B. $18,20,22,30,38,40,42$
Sample C. 18, 18, 18, 30, 42, 42, 42
Mean
Range
Standard Deviation

Sample A
(Round to two decimal places as needed.)

Step 1 ：Calculate the mean for each sample by adding all the numbers and dividing by the count of numbers. For example, for Sample A, the mean is \(\frac{18+22+26+30+34+38+42}{7} = 30\)

Step 2 ：Calculate the range for each sample by subtracting the lowest number from the highest number. For example, for Sample A, the range is \(42 - 18 = 24\)

Step 3 ：Calculate the standard deviation for each sample. First, calculate the differences from the mean, then square these differences. Next, calculate the average of these squared differences. Finally, take the square root of this average. For example, for Sample A, the differences from the mean are -12, -8, -4, 0, 4, 8, 12. The squared differences are 144, 64, 16, 0, 16, 64, 144. The average of these squared differences is \(\frac{144+64+16+0+16+64+144}{7} = 64\). The standard deviation is \(\sqrt{64} = 8\)

Step 4 ：Repeat the above steps for Sample B and Sample C. The mean and range for both samples are the same as Sample A, but the standard deviations are different. For Sample B, the standard deviation is \(\sqrt{88.57} = 9.41\). For Sample C, the standard deviation is \(\sqrt{144} = 12\)

Step 5 ：One way in which the samples are alike is that they all have the same mean and range, \(\boxed{30}\) and \(\boxed{24}\) respectively. One way in which they are different is that they have different standard deviations, indicating different levels of spread around the mean. The standard deviations are \(\boxed{8}\), \(\boxed{9.41}\), and \(\boxed{12}\) for Sample A, B, and C respectively