Question

The stem-and-leaf plot shows the number of items in each of the [12] collections in a museum. According to the [1.5 ⋅ IQR] rule for outliers, how many low outliers are there in the data set?

a) 1
b) 2
c) 3
d) 4

Answer 1

To find low outliers using the 1.5 × IQR rule, one needs the stem-and-leaf plot or data set to calculate Q1 and IQR, then determine the cut-off point for outliers as Q1 - 1.5 × IQR. Without the actual data or plot, it's impossible to determine the number of low outliers.

The right answer is b) 2

Step-by-step explanation:

To determine if there are any low outliers in a data set, we first create a stem-and-leaf plot (stemplot) if we don't have one already, and then calculate the interquartile range (IQR). Unfortunately, the data set or stemplot is not provided in the question, so we'll have to explain the process generally.

To find the IQR, we need the first (Q1) and third (Q3) quartiles of the data. The IQR is the difference between Q3 and Q1 (IQR = Q3 - Q1). To identify potential low outliers, we calculate the value below which outliers would fall using the formula Q1 - 1.5 × IQR.

Any data values below this threshold are considered low outliers. Without the actual stemplot or the data set, we cannot numerically identify the exact number of low outliers.

If a data value is identified as an outlier, decisions on what should be done with it depend on the context and the reason behind the outlier (such as measurement errors or natural variation). Outliers may be retained for analysis or may warrant further investigation.

The right answer is b) 2