Complete the chart to find the mean, variance and standard deviation. Remember to use commas and round numbers to the nearest tenth.
X _
X _
X - X _
(X - X)2
1. 900 = 466.2 = The mean is
2. 35 = -398.8 = 159,041.4 The median is
3. 500 = 66.2 = The variance is 99,667.2
4. 300 = -133.8 = The standard deviation is
Σ X = _
X = _
Σ (X - X)2 = 398,668.6
To find the mean, variance, and standard deviation, you need to follow these steps:
Step 1: Calculate the sum of all the values (ΣX).
In this case, ΣX = 900 + 35 + 500 + 300 = 1735.
Step 2: Calculate the mean.
The mean is obtained by dividing the sum of all values by the number of values. Since we have four values in this case, the mean is 1735/4 = 433.75.
Now let's complete the chart with the necessary calculations:
X | X - X | (X - X)^2
900 | 900 - 433.75 = 466.25 | (466.25)^2 = 217,804.06
35 | 35 - 433.75 = -398.75 | (-398.75)^2 = 159,004.06
500 | 500 - 433.75 = 66.25 | (66.25)^2 = 4,383.06
300 | 300 - 433.75 = -133.75 | (-133.75)^2 = 17,946.56
Step 3: Calculate the sum of the squared differences (Σ(X - X)^2).
Σ(X - X)^2 = 217,804.06 + 159,004.06 + 4,383.06 + 17,946.56 = 398,137.74.
Step 4: Calculate the variance.
The variance is obtained by dividing the sum of the squared differences by the number of values. Since we have 4 values in this case, the variance is 398,137.74/4 = 99,534.435.
Step 5: Calculate the standard deviation.
The standard deviation is the square root of the variance. Taking the square root of 99,534.435 gives us approximately 315.3 (rounded to the nearest tenth).
Now let's complete the chart:
1. 900 = 466.2 = 91,774.7 The mean is approximately 433.8.
2. 35 = -398.8 = 159,004.1 The median is approximately -398.8.
3. 500 = 66.2 = 99,534.4 The variance is approximately 99,534.4.
4. 300 = -133.8 = 315.3 The standard deviation is approximately 315.3.
Lastly, ΣX = 1735, representing the sum of all the values,
X = 433.8, representing the mean,
and Σ(X - X)^2 = 398,668.6, representing the sum of the squared differences.