Ricardo collected data on the prices of items at two gift shops in his town. He rounded each price to the nearest dollar and displayed the prices in the line plots below.
Store A Prices (Nearest $)
Store B Prices (Nearest $)
The mean absolute deviation for both stores is approximately
. How many times as great as the MAD is the difference in means for the two stores? Round to the nearest tenth.
Responses
A. 5.4
B. 5.8
C. 7
D. 14.5
To find the mean absolute deviation (MAD), we first need to find the mean for each store.
Store A mean: (1+2+2+2+3+3+3+4+4+4)/10 = 24/10 = 2.4
Store B mean: (0+1+2+2+3+3+3+5+5+6)/10 = 30/10 = 3
Next, we find the absolute deviations for each data point from the mean:
Store A deviations: (|1-2.4|, |2-2.4|, |2-2.4|, |2-2.4|, |3-2.4|, |3-2.4|, |3-2.4|, |4-2.4|, |4-2.4|, |4-2.4|)
= (1.4, 0.4, 0.4, 0.4, 0.6, 0.6, 0.6, 1.6, 1.6, 1.6)
Store B deviations: (|0-3|, |1-3|, |2-3|, |2-3|, |3-3|, |3-3|, |3-3|, |5-3|, |5-3|, |6-3|)
= (3, 2, 1, 1, 0, 0, 0, 2, 2, 3)
Find the sum of the absolute deviations for each store and divide by the number of data points to find the MAD:
Store A MAD: (1.4 + 0.4 + 0.4 + 0.4 + 0.6 + 0.6 + 0.6 + 1.6 + 1.6 + 1.6) / 10 = 7.6 / 10 = 0.76
Store B MAD: (3 + 2 + 1 + 1 + 0 + 0 + 0 + 2 + 2 + 3) / 10 = 14 / 10 = 1.4
The difference in means between the two stores is |2.4 - 3| = 0.6.
To find how many times as great the difference in means is compared to the MAD, we divide the difference in means by the MAD for Store A: 0.6 / 0.76 = 0.79
Therefore, the answer is closest to 0.8, which is not one of the given options.