Step 1: Put the numbers in order. 1, 2, 5, 6, 7, 9, 12, 15, 18, 19, 27.
Step 2: Find the median. 1, 2, 5, 6, 7, 9, 12, 15, 18, 19, 27. Step 3: Place parentheses around the numbers above and below the median. Not necessary statistically, but it makes Q1 and Q3 easier to spot. (1, 2, 5, 6, 7), 9, (12, 15, 18, 19, 27). Step 4: Find Q1 and Q3 Think of Q1 as a median in the lower half of the data and think of Q3 as a median for the upper half of data. (1, 2, 5, 6, 7), 9, ( 12, 15, 18, 19, 27). Q1 = 5 and Q3 = 18. Step 5: Subtract Q1 from Q3 to find the interquartile range. 18 – 5 = 13.
You survey households in your area to find the average rent they are paying. Find the standard deviation from the following data: $1550, $1700, $900, $850, $1000, $950. Step 1: Find the mean: ($1550 + $1700 + $900 + $850 + $1000 + $950)/6 = $1158.33 Step 2: Subtract the mean from each value. This gives you the differences: $1550 – $1158.33 = $391.67 $1700 – $1158.33 = $541.67 $900 – $1158.33 = -$258.33 $850 – $1158.33 = -$308.33 $1000 – $1158.33 = $158.33 $950 – $1158.33 = $208.33 Step 3: Square the differences you found in Step 3: $391.672 = 153405.3889 $541.672 = 293406.3889 -$258.332 = 66734.3889 -$308.332 = 95067.3889 $158.332 = 25068.3889 $208.332 = 43401.3889 Step 4: Add up all of the squares you found in Step 3 and divide by 5 (which is 6 – 1): (153405.3889 + 293406.3889 + 66734.3889 + 95067.3889 + 25068.3889 + 43401.3889) / 5 = 135416.66668
Step 5: Find the square root of the number you found in Step 4 (the variance): √135416.66668 = 367.99
The standard deviation is 367.99.
Reason: It assumes that the input variable is independent, but in real world it is unrealistic, since all the features would be dependent on each other.