Mean variance and standard deviation for frequency distribution
Answers
Step-by-step explanation:
You and your friends have just measured the heights of your dogs (in millimeters):
The heights (at the shoulders) are: 600mm, 470mm, 170mm, 430mm and 300mm.
Find out the Mean, the Variance, and the Standard Deviation.
Your first step is to find the Mean:
Answer:
Mean=600 + 470 + 170 + 430 + 3005 =19705 =394
so the mean (average) height is 394 mm. Let's plot this on the chart:
Now we calculate each dog's difference from the Mean:
To calculate the Variance, take each difference, square it, and then average the result:
Varianceσ2=2062 + 762 + (−224)2 + 362 + (−94)25 =42436 + 5776 + 50176 + 1296 + 88365 =1085205 =21704
So the Variance is 21,704
And the Standard Deviation is just the square root of Variance, so:
Standard Deviationσ=√21704 =147.32... =147 (to the nearest mm)
Mean is the sum of the values divided by the total number.
Variation is considered the measure of dispersion which accounts for the spread of all data in a data sheet.
Standard deviation is the square root of the variance
- Steps for calculating mean, variance, and standard deviation of the set of data: 10,20,30,40
- Calculate the mean.
- Total amount divided by total number = (10+20+30+40)/4
- = 100/4 = 25
- Subtract the mean from each value in the given set
- 10-25 = -15
- 20-25 = -5
- 30-25 = 5
- 40-25 =15
- Take the square of each of the resulting values.
- (-15)² =225 (-5)² =25 (5)² =25 (15)² = 225
- Take the sum of the squares = 25+25+225+225 = 500
- Divide this total by the number of set of values (variance, S2) = 500/4 = 125
- Take the positive square root of the variance (standard deviation, S) = 11.18
#SPJ2