Question

journalists try to use shorter or simpler words in their news stories whenever possible. the box below shows the number of letters in each word taken from one sentence in a news article. what are the mean and median number of letters per word? what is the outlier? the mean number of letters per word = the median number of letters per word = the outlier = there is no outlier

Explanation:

Step1: List out the data

The data values from the stem - and - leaf plot are: 11, 17, 22, 26, 38, 89.

Step2: Calculate the mean

The mean $\bar{x}=\frac{11 + 17+22+26+38+89}{6}=\frac{203}{6}\approx33.83$.

Step3: Arrange data in ascending order for median

The data in ascending order is 11, 17, 22, 26, 38, 89. Since $n = 6$ (an even number of data points), the median $M=\frac{22 + 26}{2}=24$.

Step4: Check for outlier

We can use the 1.5(IQR) rule. First, find the first quartile $Q_1$ and the third quartile $Q_3$. For $n = 6$, the lower half of the data is 11, 17, 22 and $Q_1 = 17$. The upper half of the data is 26, 38, 89 and $Q_3=38$. The inter - quartile range $IQR=Q_3 - Q_1=38 - 17 = 21$. Then $1.5\times IQR=1.5\times21 = 31.5$. $Q_1-1.5\times IQR=17 - 31.5=-14.5$ and $Q_3 + 1.5\times IQR=38+31.5 = 69.5$. Since $89>69.5$, the outlier is 89.

Answer:

The mean number of letters per word = 33.83
The median number of letters per word = 24
The outlier = 89