Final answer:
To find the mean deviation, calculate the mean, then the average absolute deviation from the mean, which is 1.2. For the standard deviation, calculate the mean of squared deviations from the mean and take the square root, resulting in approximately 1.58.
Step-by-step explanation:
To calculate the mean deviation and standard deviation of the given data set (1, 2, 4, 3, 5), follow these steps:
- Calculate the mean (×) of the data set by adding all the numbers and dividing by the number of items. Mean = (1 + 2 + 4 + 3 + 5) / 5 = 15 / 5 = 3.
- Find the absolute deviations of each data point from the mean, which are |1-3|, |2-3|, |4-3|, |3-3|, and |5-3|, equals to 2, 1, 1, 0, and 2, respectively.
- The mean deviation is the average of these absolute deviations. So Mean Deviation = (2 + 1 + 1 + 0 + 2) / 5 = 6 / 5 = 1.2.
- For standard deviation, square each of the deviations found in step 2 to get 4, 1, 1, 0, and 4, respectively.
- Sum up these squares and find the average (since this is a sample, not a population, we divide by n-1 instead of n): (4 + 1 + 1 + 0 + 4) / (5 - 1) = 10 / 4 = 2.5.
- Take the square root of this average to get the standard deviation, which is √2.5 ≈ 1.58.
The mean deviation is 1.2 and the standard deviation is approximately 1.58.