11 grade maths others
The variance of the data 6, 8, 10, 12, 14, 16, 18, 20, 22, 24 is :
- A. 15
- B. 20
- C. 30
- D. 33
The variance of the data 6, 8, 10, 12, 14, 16, 18, 20, 22, 24 is :
- A. 15
- B. 20
- C. 30
- D. 33
1 Answer
Askiitians Tutor Team
Approved Tutor Answer9 Months agoTo find the variance of the given data set (6, 8, 10, 12, 14, 16, 18, 20, 22, 24), follow these steps:
Step 1: Calculate the Mean
The mean (average) is calculated by adding all the numbers together and dividing by the total count.
- Sum = 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24 = 180
- Count = 10
- Mean = 180 / 10 = 18
Step 2: Find the Squared Differences
Next, subtract the mean from each number and square the result:
- (6 - 18)² = 144
- (8 - 18)² = 100
- (10 - 18)² = 64
- (12 - 18)² = 36
- (14 - 18)² = 16
- (16 - 18)² = 4
- (18 - 18)² = 0
- (20 - 18)² = 4
- (22 - 18)² = 16
- (24 - 18)² = 36
Step 3: Calculate the Variance
Add all the squared differences together and divide by the number of data points:
- Sum of squared differences = 144 + 100 + 64 + 36 + 16 + 4 + 0 + 4 + 16 + 36 = 420
- Variance = 420 / 10 = 42
Final Answer
The variance of the data set is 42. Since this value is not listed among the options (A. 15, B. 20, C. 30, D. 33), it appears there may be an error in the provided choices.
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