Question

which of these statements about the histogram is/are true? i. there are no outliers in the data. ii. there are no gaps in the data. iii. the mean is less than the median. iv. the data is symmetric. a i only b i and ii only c i, ii, and iv only d ii and iv only e i, ii, iii, and iv

Explanation:

Step1: Check for outliers

Outliers are data - points that are far from the rest of the data. In the histogram, all the bars are adjacent and there are no extreme values far from the main cluster of data, so there are no outliers. Statement I is true.

Step2: Check for gaps

Gaps in a histogram mean there are no data - points in a particular interval. Here, the bars are adjacent, so there are no gaps in the data. Statement II is true.

Step3: Analyze mean and median

The histogram is right - skewed (tail on the right side). In a right - skewed distribution, the mean is greater than the median. So, statement III is false.

Step4: Check for symmetry

The histogram is not symmetric as the right - hand side of the distribution has a longer tail compared to the left - hand side. So, statement IV is false.

Answer:

B. I and II only