Question

1. two data sets are shown below. data set a: 12, 18, 25, 30, 30, 34 data set b: 10, 15, 20, 35, 40, 45 what is the mean for data set a? what is the mean for data set b? what is the range for data set a? what is the range for data set b? write a \t\ or \f\ to indicate whether the statements are true or false: data set a has the higher mean. data set b has the higher mean data set a has the wider range. data set a and data set b have the same range.

Explanation:

Step1: Calculate mean of Data Set A

Data Set A: 12,18,25,30,30,34. Sum = 12+18+25+30+30+34 = 149. Mean = $\frac{149}{6} \approx 24.83$

Step2: Calculate mean of Data Set B

Data Set B:10,15,20,35,40,45. Sum =10+15+20+35+40+45=165. Mean = $\frac{165}{6}=27.5$

Step3: Calculate range of Data Set A

Range = max - min =34-12=22

Step4: Calculate range of Data Set B

Range = max - min=45-10=35

Step5: Compare means

Data Set B's mean (27.5) > Data Set A's mean (≈24.83)

Step6: Compare ranges

Data Set B's range (35) > Data Set A's range (22)

Answer:

Mean of Data Set A: ≈24.83
Mean of Data Set B:27.5
Range of Data Set A:22
Range of Data Set B:35
Data Set A has the higher mean? F
Data Set B has the higher mean? T
Data Set A has the wider range? F
Data Set A and Data Set B have the same range? F