Question

examine the two data sets below.
data set 1: 23, 34, 45, 46, 48, 49, 54, 56, 67, 78
data set 2: 23, 24, 45, 48, 48, 49, 49, 56, 77, 78
which 2 statements about the data sets are true?
a data set 1 has a greater iqr than data set 2.
b data set 1 has a greater median than data set 2.
c both data sets have the same range.
d data set 1 has a greater mean than data set 2.

Explanation:

Step1: Calculate the range

For Data Set 1: Range = \(78 - 23=55\)
For Data Set 2: Range = \(78 - 23 = 55\)

Step2: Calculate the median

Data Set 1 has \(n = 10\) data points. Median=\(\frac{48 + 49}{2}=48.5\)
Data Set 2 has \(n = 10\) data points. Median=\(\frac{48+49}{2}=48.5\)

Step3: Calculate the IQR

For Data Set 1:
Lower half: \(23,34,45,46,48\). \(Q_1 = 45\)
Upper half: \(54,56,67,78\). \(Q_3=67\)
IQR=\(67 - 45=22\)
For Data Set 2:
Lower half: \(23,24,45,48,48\). \(Q_1 = 45\)
Upper half: \(49,49,56,77,78\). \(Q_3 = 56\)
IQR=\(56 - 45 = 11\)

Step4: Calculate the mean

For Data Set 1:
Mean=\(\frac{23+34 + 45+46+48+49+54+56+67+78}{10}=\frac{500}{10}=50\)
For Data Set 2:
Mean=\(\frac{23+24+45+48+48+49+49+56+77+78}{10}=\frac{497}{10}=49.7\)

Answer:

A. Data Set 1 has a greater IQR than Data Set 2.
C. Both data sets have the same Range.
D. Data Set 1 has a greater mean than Data Set 2.