We are given a boxplot and a histogram of the number of colds patients had experienced over the last year.
Let us analyze each of the given statements.
Statement 1: Both displays show the data is skewed right.
The above statement is correct.
Notice that the peak of the histogram is at 2 and the long tail of values is to the right of the peak.
Hence, the histogram is skewed right.
Now, notice the boxplot, the whisker is longer on the right side of the box.
Hence, the distribution of the boxplot is skewed right.
Statement 2: Both displays show the data is skewed left.
The above statement is incorrect. (because statement 1 is correct)
Statement 3: Only the histogram indicates the number of patients in the sample.
The above statement is correct.
You can calculate the total number of patients in the sample by adding up the heights of all bars in the histogram.
On the other hand, there is no indication of the number of patients in the boxplot.
Statement 4: The box plot shows the mean number of colds was 2.
The above statement is incorrect because a box plot gives us the median value, not the mean.
Statement 5: The box plot shows the median number of colds was 2.
The above statement is correct.
The median of the box plot is the middle value of the box which is exactly 2.
Hence, the median of the box plot is 2.
Summary:
Statements 1, 3, and 5 are correct.
