Question

Study the following stem-and-leaf plot for the ages of different members of a country club. Which of the following statements is true?


Statement I: The center of the given data is $34$.
Statement II: The outlier of the data given is $61$.
Statement III: The spread of the ages is from $22$ years to $61$ years.

• A. Statement I and statement II
• B. None of the statements is true
• C. Only statement III
• D. Statement I and statement III

Answer 1

The correct option is C Only statement III

Let’s check the options.
Using the plot, we can see that there are 15 data values.
$22,28,29,30,34,35,37,40,44,50,54,57,59,60,61$
There are $7$ values to the left of $40$ and $7$ values to the right of $40$. So, the middle value of the data set is $40$. So, the center of the plot is $40$ years. Hence, statement I is false.
An outlier is a data value that is numerically distant from the data set, or it is a value that is very different from the rest of the values in the data set.
Using the key, we can see that there are 15 data values: $22,28,29,30,34,35,37,40,44,50,54,57,59,60,61.$
All of them are close to each other. None of the values are numerically distant from the data set. Hence, there is no outlier for the data set. Hence, statement II is false.

To know the spread of data sets, we should know the maximum and the minimum value.
Maximum value $=61$
Minimum value $=22$
Therefore, we can say that the spread of the ages is from $22$ years to 61 years.
Hence, statement III is true.