In: Statistics and Probability
Base your answers to questions 1-3 on the following scenario: Suppose a paper company randomly chooses 10 days from their past quarter to see how many units were being shipped on weekdays (D) and weekends (E) by the company.
Units | 165 | 140 | 120 | 230 | 145 | 235 | 125 | 180 | 150 | 210 |
Day | D | D |
D |
E | D | E | D | D | D | E |
1. What is the sample variance of the amount of units shipped on a weekend by this company and what is the sample mean amount of units shipped on a weekday by this company?
2. What kind of plot would be appropriate for visualizing mean number units shipped based on day type (weekend or weekday).
3. The first quartile of the units shipped per day is 141.25, and the third quartile was 202.5. Based on the interquartile range, would you suspect a day where 260 units are sold to be an outlier?
Solution-1:
day(E) | XBAR | E-XBAR | (E-Xbar)^2 |
230 | 225 | 5 | 25 |
235 | 225 | 10 | 100 |
210 | 225 | -15 | 225 |
TOTAL | 350 |
sample variance=
s^2=350/3-1
s^2=175
sample variance for weekend=175 units
what is the sample mean amount of units shipped on a weekday by this company?
d |
165 |
140 |
120 |
145 |
125 |
180 |
150 |
d=sum of d/total d
=1025/7
=146.4286
the sample mean amount of units shipped on a weekday by this company=146.4286
2. What kind of plot would be appropriate for visualizing mean number units shipped based on day type (weekend or weekday).
comparative box plot would be appropriate
3. The first quartile of the units shipped per day is 141.25, and the third quartile was 202.5. Based on the interquartile range, would you suspect a day where 260 units are sold to be an outlier?
IQR=Q3-Q1=202.5-141.25
IQR=61.25
LOWER FENCE=Q1-1.5IQR=141.25-1.5*61.25=49.375
UPPER FENCE=Q3+1.5IQR=202.5+1.5*61.25= 294.375
value below lower fence is outlier
value above upper fence is outlier
260 falls in the range'
49.375<260<294.375
260 IS NOT AN OUTLIER