use the data set to determine which statements are correct. check all that apply. 115,120,118,104,109,148,135…

use the data set to determine which statements are correct. check all that apply. 115,120,118,104,109,148,135,141,139 the median is 120. the median is 109. there is an outlier. the lower quartile is 118. the lower quartile is 112. the upper quartile is 140. the upper quartile is 141. the interquartile range is 28.

use the data set to determine which statements are correct. check all that apply. 115,120,118,104,109,148,135,141,139 the median is 120. the median is 109. there is an outlier. the lower quartile is 118. the lower quartile is 112. the upper quartile is 140. the upper quartile is 141. the interquartile range is 28.

Answer

Explanation:

Step1: Arrange data in ascending order

104, 109, 115, 118, 120, 135, 139, 141, 148

Step2: Calculate the median

There are 9 data - points. The median is the 5th value. So, median = 120.

Step3: Calculate the lower half

The lower half is 104, 109, 115, 118. The lower quartile ($Q_1$) is the median of the lower half. Since there are 4 values, $Q_1=\frac{109 + 115}{2}=112$.

Step4: Calculate the upper half

The upper half is 135, 139, 141, 148. The upper quartile ($Q_2$) is the median of the upper half. Since there are 4 values, $Q_2=\frac{139+141}{2}=140$.

Step5: Calculate the inter - quartile range (IQR)

$IQR = Q_2 - Q_1=140 - 112 = 28$.

Step6: Check for outliers

The lower fence for outliers is $Q_1-1.5\times IQR=112-1.5\times28=112 - 42 = 70$. The upper fence for outliers is $Q_2 + 1.5\times IQR=140+1.5\times28=140 + 42 = 182$. Since all data - points are within these fences, there are no outliers.

Answer:

The median is 120. The lower quartile is 112. The upper quartile is 140. The interquartile range is 28.