Question

the dotplots below show the amounts of money the same group of 30 shoppers spent on groceries in october and in december. amounts are rounded to the nearest ten dollars. part a calculate the median of each distribution. october median: december median:

Explanation:

Step1: Count the number of data points

There are 30 data points (shoppers). For a set with \(n = 30\) data points, the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+ 1)\)th ordered data points. \(\frac{30}{2}=15\), so we need the 15th and 16th ordered data points.

Step2: Find the 15th and 16th data points for October

Count the dots in the October dot - plot:

• Cumulative counts:
• Up to \(100: 3\)
• Up to \(120: 3 + 3=6\)
• Up to \(140:6 + 3 = 9\)
• Up to \(160:9+4 = 13\)
• Up to \(180:13 + 4=17\)

The 15th and 16th data points are in the \(180\) group.

Step3: Find the 15th and 16th data points for December

Count the dots in the December dot - plot:

• Cumulative counts:
• Up to \(100: 2\)
• Up to \(120:2 + 3=5\)
• Up to \(140:5 + 3 = 8\)
• Up to \(160:8+4 = 12\)
• Up to \(180:12 + 4=16\)

The 15th and 16th data points are in the \(200\) group.

Answer:

October Median: \(180\)
December Median: \(200\)