Question

1. two measures of center are marked on the density curve shown. which of the following is correct? (a) the median is at the solid line and the mean is at the dashed line. (b) the median is at the dashed line and the mean is at the solid line. (c) the mode is at the dashed line and the median is at the solid line. (d) the mode is at the solid line and the median is at the dashed line. (e) the mode is at the dashed line and the mean is at the solid line. 6. the cumulative relative frequency graph at right shows the distribution of lengths (in centimeters) of fingerlings at a fish hatchery. the interquartile range for this distribution is approximately: (a) 0.18 to 0.85 centimeters (b) 5 to 7 centimeters (c) 5.5 to 6.7 centimeters (d) 1.2 centimeters (e) 2 centimeters

Explanation:

Step 1: Recall properties of mode, median and mean in a skewed - right distribution

In a right - skewed distribution, the mode is the peak of the density curve. The median is the value that divides the area under the density curve into two equal parts. The mean is pulled in the direction of the long tail. So, the mode is at the left - most of these three measures, the median is in the middle, and the mean is at the right - most. The solid line is at the peak (mode) and the dashed line is to the right of it (median).

Step 2: Analyze the inter - quartile range (IQR) from the cumulative relative frequency graph

The inter - quartile range is \(Q_3 - Q_1\). To find \(Q_1\) (the 25th percentile) and \(Q_3\) (the 75th percentile) on a cumulative relative frequency graph:

• Locate the cumulative relative frequency of 0.25 and 0.75 on the y - axis.
• Draw horizontal lines from these points to the curve, then draw vertical lines down to the x - axis to get the values of \(Q_1\) and \(Q_3\).
• From the graph, \(Q_1\approx5.5\) and \(Q_3\approx6.7\).
• Then \(IQR = Q_3 - Q_1\approx6.7 - 5.5=1.2\)

Answer:

1. d) The mode is at the solid line and the median is at the dashed line.
2. d) 1.2 centimeters