Answer to Question #145201 in Statistics and Probability for Christian Selma

Question

A survey was taken among college students as to how many minutes they play a newly released online game, Genshin Impact, per day. Using UNGROUPED statistical analysis, calculate the following:

a.) Mean, Median, and Mode,

b.) Variance and Standard Deviation.
Time(Mins)
174
300
204
185
326
158
300
280
210
194
345
347
339
300
187
329
184
275
180
136

Answer 1

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