Question

the plots 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: 180 december median: 190 part b compare the center and spread for the two distributions.

Explanation:

Step1: Recall median formula

For a set of $n = 30$ (an even - numbered data set), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+ 1)$th ordered data values.

Step2: Find position for October

For $n = 30$, $\frac{n}{2}=15$ and $\frac{n}{2}+1 = 16$. We order the data values of the amount spent on groceries in October and find the 15th and 16th values. From the dot - plot, we assume we have ordered data. If we count the dots, we find the median value. Since the answer for October median is given as 180, we assume the 15th and 16th ordered values average to 180.

Step3: Find position for December

Again, for $n = 30$ (the same number of shoppers), $\frac{n}{2}=15$ and $\frac{n}{2}+1 = 16$. Counting the dots in the December dot - plot, we find the 15th and 16th ordered values. Given the answer for December median is 190, the average of the 15th and 16th ordered values is 190.

Step4: Compare center and spread for Part B

Center: The median for October is 180 and for December is 190. So, the center (median) of the amount spent on groceries is higher in December than in October.
Spread: To compare the spread, we can look at the range (difference between the maximum and minimum values) or the inter - quartile range (IQR). Without exact values of the minimum, maximum, Q1 and Q3, we can make a rough estimate from the dot - plots. If the dots are more spread out in a plot, the spread is larger. Visually, if the December dot - plot has dots more spread out than the October dot - plot, the spread in December is larger; if they are similar in spread, we can say the spreads are comparable.

Answer:

Part A: October Median: 180, December Median: 190
Part B: Center: The median amount spent on groceries is higher in December (190) than in October (180). Spread: (Describe based on visual inspection of dot - plots, e.g., If December dots are more spread out: The spread of the amount spent on groceries is larger in December than in October; if similar: The spreads of the amount spent on groceries in October and December are comparable)