Question

question 4 1 pts consider a data set comprised of exam scores where the following summary measures are computed: minimum = 50, q1 = 72, median = 79, q3 = 79, maximum = 98. what conclusion can we draw about this data set based on these summary measures? the value of 98 must be an outlier. the distribution of exam scores is symmetric. at least 25% of the exam scores are equal to 79. the iqr must be equal to 0. none of the above conclusions are correct.

Explanation:

Step1: Recall quartile and median concepts

The median divides data into two - halves. $Q_1$ is the first - quartile (25th percentile), the median is the 50th percentile, and $Q_3$ is the third - quartile (75th percentile).

Step2: Analyze the given values

We have $Q_1 = 72$, Median=$79$, $Q_3 = 79$. The inter - quartile range (IQR) is $IQR=Q_3 - Q_1=79 - 72 = 7
eq0$. So the statement about $IQR = 0$ is wrong.

Step3: Check for outliers

To check for outliers, we use the fences: Lower fence $=Q_1-1.5\times IQR=72-1.5\times7 = 72 - 10.5=61.5$, Upper fence $=Q_3 + 1.5\times IQR=79+1.5\times7=79 + 10.5 = 89.5$. Since $98>89.5$, 98 is an outlier, but we cannot say "must be" just based on these summary statistics without more information about the data set.

Step4: Check for symmetry

For a symmetric distribution, the distance from $Q_1$ to the median should be equal to the distance from the median to $Q_3$. Here, $79 - 72
eq79 - 79$, so the distribution is not symmetric.

Step5: Analyze the value of 79

The median is 79 and $Q_3$ is 79. This means that at least 25% of the data (from the median to $Q_3$) has a value of 79.

Answer:

At least 25% of the exam scores are equal to 79.