Find variance and standard deviation for the data
35,45,30,35,40,25
To find the variance and standard deviation of a data set, we need to follow these steps:
Step 1: Calculate the mean (average) of the data set.
Step 2: Calculate the deviation of each data point from the mean.
Step 3: Square each deviation.
Step 4: Calculate the sum of all the squared deviations.
Step 5: Divide the sum of squared deviations by the number of data points.
Step 6: Take the square root of the variance to find the standard deviation.
Let's calculate the variance and standard deviation for the given data set: 35, 45, 30, 35, 40, 25.
Step 1: Calculate the mean:
Mean = (35 + 45 + 30 + 35 + 40 + 25) / 6 = 210 / 6 = 35.
Step 2: Calculate the deviation of each data point from the mean:
35 - 35 = 0
45 - 35 = 10
30 - 35 = -5
35 - 35 = 0
40 - 35 = 5
25 - 35 = -10
Step 3: Square each deviation:
0² = 0
10² = 100
(-5)² = 25
0² = 0
5² = 25
(-10)² = 100
Step 4: Calculate the sum of squared deviations:
0 + 100 + 25 + 0 + 25 + 100 = 250
Step 5: Divide the sum of squared deviations by the number of data points:
Variance = 250 / 6 = 41.67
Step 6: Take the square root of the variance to find the standard deviation:
Standard Deviation = √41.67 ≈ 6.45
Therefore, the variance is approximately 41.67 and the standard deviation is approximately 6.45 for the given data set.
To find the variance and standard deviation for the given data, follow these steps:
Step 1: Find the mean.
To find the mean, add up all the values and divide by the number of values.
(35 + 45 + 30 + 35 + 40 + 25) / 6 = 210 / 6 = 35
Step 2: Find the difference between each value and the mean.
Subtract the mean from each value.
(35 - 35 = 0), (45 - 35 = 10), (30 - 35 = -5), (35 - 35 = 0), (40 - 35 = 5), (25 - 35 = -10)
Step 3: Square each difference.
Square each difference calculated in Step 2.
0^2 = 0, 10^2 = 100, (-5)^2 = 25, 0^2 = 0, 5^2 = 25, (-10)^2 = 100
Step 4: Find the sum of all squared differences.
Add up all the squared differences calculated in Step 3.
0 + 100 + 25 + 0 + 25 + 100 = 250
Step 5: Find the variance.
To find the variance, divide the sum of squared differences by the number of values.
250 / 6 = 41.67 (rounded to two decimal places)
Step 6: Find the standard deviation.
To find the standard deviation, take the square root of the variance.
√41.67 ≈ 6.45 (rounded to two decimal places)
Therefore, the variance of the given data is approximately 41.67 and the standard deviation is approximately 6.45.