Question

a shelter kept track of the number of dogs adopted each day for three weeks. use the table to find the statistical measures. mean: 6.29 median: mode: 6 range: 7 8 9

Explanation:

Step1: Find the number of data points

There are \(3\times7 = 21\) data points.

Step2: Find the median

Since \(n = 21\) (odd), the median is the \(\frac{n + 1}{2}=\frac{21+ 1}{2}=11^{th}\) data point.
Counting the data points: \(2\) of \(3\), \(3\) of \(4\), \(2\) of \(5\), \(3\) of \(6\), \(4\) of \(7\), \(5\) of \(8\), \(2\) of \(9\).
The cumulative counts: \(2+3 + 2+3=10\) (for \(3,4,5,6\)), the \(11^{th}\) data point is \(7\).

Step3: Find the mode

The mode is the number that appears most frequently.
Count the frequencies: \(3\) appears \(2\) times, \(4\) appears \(3\) times, \(5\) appears \(2\) times, \(6\) appears \(3\) times, \(7\) appears \(4\) times, \(8\) appears \(5\) times, \(9\) appears \(2\) times.
The number \(8\) has the highest frequency.

Step4: Find the range

The range is \(max - min\).
The maximum value is \(9\) and the minimum value is \(3\). So \(range=9 - 3=6\).

Answer:

Median: \(7\), Mode: \(8\), Range: \(6\)