Given data in ascending order:
136,158, 174, 180, 184, 185, 187, 194, 204, 210, 275, 280, 300, 300, 300, 326, 329, 339, 345, 347
n=20
Mean:
"\\bar x=\\frac{\\sum x}{n}=\\frac{136+158+174+180+184+185+187+194+204+210+275+280+300+300+300+326+329+339+345+347}{20}=247.65"
Median is a value separating the higher half from the lower half of a data sample, thus median is the mean of the middle two numbers:
"median = \\frac{210+275}{2}=242.5"
Mode is the most frequent value in data set:
mode = 300
Variance:
"s^2=\\frac{\\sum{(x-\\bar x)^2}}{n-1}"
"s^2=\\frac{(136-247.65)^2+...+(347-247.65)^2}{20-1}=5201.29"
Standard deviation:
"s=\\sqrt{\\frac{\\sum{(x-\\bar x)^2}}{n-1}}" or "s=\\sqrt{variance}"
"s=\\sqrt{5201.29}=72.12"
Answer:
a) mean = 247.65, median = 242.5, mode = 300
b) variance = 5201.29, standard deviation = 72.12
Comments
Leave a comment