Question

Statistics Q. The number of calls received per hour at a call centre by a sample of different operators are given below: 5,4,7,6,8,10,11,0,7,18 1. Find the arithmetic mean and median and standard deviation. 2. If the last observation is 28 instead of 18, how will the mean and median change? 3. Calculate a 15% trimmed mean

Answer 1

1 arithmetic mean: $(5+4+7+6+8+10+11+0+7+18+1)/11=7$

median: 7; standard deviation:  $\sqrt{\frac{(0-11)^2+(1-11)^2+(4-11)^2+(5-11)^2+(6-11)^2+(7-11)^2+(7-11)^2+(8-11)^2+(10-11)^2+(11-11)^2+(18-11)^2}{11-1}}=9$

2 arithmetic mean: $(5+4+7+6+8+10+11+0+7+28+1)/11=7.9$

median: 7

3 $k=11*0.15=1.65$ ; $R=11-2*1.65=7.7$

trimmed mean: $\frac{1}{7.7}*(1*0.65+4+5+6+7+7+8+10+11*0.65)=7.12$