Answer :
The variance of the data set 198, 190, 245, 211, 193, 193 is approximately 366.33.
To find the variance of a set of data, you can follow these steps:
Calculate the mean (average) of the data.
Subtract the mean from each data point to find the deviation of each data point from the mean.
Square each of these deviations.
Find the mean of the squared deviations to obtain the variance.
Let's apply these steps to your data set: 198, 190, 245, 211, 193, 193.
Step 1: Calculate the mean (average):
(198 + 190 + 245 + 211 + 193 + 193) / 6 = 1230 / 6 = 205
Step 2: Find the deviation of each data point from the mean:
For 198: 198 - 205 = -7
For 190: 190 - 205 = -15
For 245: 245 - 205 = 40
For 211: 211 - 205 = 6
For 193: 193 - 205 = -12
For 193: 193 - 205 = -12
Step 3: Square each of these deviations:
(-7)² = 49
(-15)² = 225
(40)² = 1600
(6)² = 36
(-12)² = 144
(-12)² = 144
Step 4: Find the mean of the squared deviations:
(49 + 225 + 1600 + 36 + 144 + 144) / 6 = 2198 / 6 = 366.33 (rounded to two decimal places)
So, the variance of the data set 198, 190, 245, 211, 193, 193 is approximately 366.33.
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