Question

The hourly earnings (in dollars) for a sample of 25 railroad equipment manufacturers are: 1. 15.60 18.75 14.60 15.80 14.35 13.90 17.50 17.55 13.80 14.20 19.05 15.35 15.20 19.45 15.95 16.50 16.30 15.25 15.05 19.10 15.20 16.22 17.75 18.40 15.25 Find the median and the mode(s) (if they exist) of the data. What is the interquartile range? Give a box-and-whisker plot of the data Give the formulas to calculate the simple mean and the sample standard deviation then determine them. Median: (4pta) Mode: (4pta) Ql Q2= Q3 IQR= (4pta) Box-and-whisker plot: (Gpta) Mean: (4pta) Formula Value: Standard deviation: (Geta) Formula: Value

Answer 1

$Median=15.800,~Mode=15.2,~15.25~(both~have~highest~frequency~i.e.~2),\\ Q1=15.125,~Q2=15.800,~Q3=17.650,~IQR=2.525.$

Boxplot of Hourly earning 20 18 17 16 15 14 13- Hourly earning 19

$Mean=\mu=\frac{1}{25}\sum_{i=1}^{25}x_i=16.243\\ \sigma=Standard~deviation=\sqrt{\frac{1}{25}\sum_{i=1}^{25}(x_i-\mu)^2}=1.731.$