Answer:
Explanation:
Step 1: Find the mean (average) of the data.
To find the mean, we add up all the scores and divide by the total number of students.
(2 * 100 + 4 * 90 + 5 * 80 + 3 * 70 + 1 * 60) / (2 + 4 + 5 + 3 + 1) = 78
Step 2: Find the difference between each score and the mean.
For each score, subtract the mean from the score. This gives us the deviation.
Deviation from 100: 100 - 78 = 22
Deviation from 90: 90 - 78 = 12
Deviation from 80: 80 - 78 = 2
Deviation from 70: 70 - 78 = -8
Deviation from 60: 60 - 78 = -18
Step 3: Square each deviation.
Square each deviation to eliminate negative values and emphasize differences.
Squared deviation from 100: 22^2 = 484
Squared deviation from 90: 12^2 = 144
Squared deviation from 80: 2^2 = 4
Squared deviation from 70: (-8)^2 = 64
Squared deviation from 60: (-18)^2 = 324
Step 4: Find the sum of the squared deviations.
Add up all the squared deviations.
484 + 144 + 4 + 64 + 324 = 1020
Step 5: Divide the sum of squared deviations by the number of data points.
Divide the sum of squared deviations by the total number of students.
1020 / 15 = 68
Step 6: Round the variance to the nearest hundredth.
The variance is 68.00 when rounded to the nearest hundredth.
Therefore, the variance of the data is 68.00.