Question

6 from unit 3, lesson 12 the dot plots display the height, rounded to the nearest foot, of maple trees from two different tree farms. two dot plots are shown, each with a number line from 3 to 14 labeled height (feet). the first dot plot has dots: 1 at 6, 2 at 7, 3 at 8, 2 at 9, 1 at 10. the second dot plot has dots: 1 at 4, 2 at 6, 3 at 8, 2 at 10, 1 at 12. a. compare the mean and standard deviation of the two data sets. b. what does the standard deviation tell you about the trees at these farms?

Explanation:

Step1: Count data points for both plots

Top plot: 1(6)+2(7)+4(8)+2(9)+1(10) = 10 points
Bottom plot:1(4)+2(6)+3(8)+2(10)+1(12) =9 points

Step2: Calculate mean of top plot

Mean = $\frac{(6×1)+(7×2)+(8×4)+(9×2)+(10×1)}{10}$ = $\frac{6+14+32+18+10}{10}$ = $\frac{80}{10}$ = 8

Step3: Calculate mean of bottom plot

Mean = $\frac{(4×1)+(6×2)+(8×3)+(10×2)+(12×1)}{9}$ = $\frac{4+12+24+20+12}{9}$ = $\frac{72}{9}$ =8

Step4: Compare standard deviation

Top plot data: 6,7,7,8,8,8,8,9,9,10 (clustered around 8)
Bottom plot data:4,6,6,8,8,8,10,10,12 (spread wider from 4 to12)
Wider spread → higher standard deviation

Answer:

a. The means of both data sets are equal (8 feet). The standard deviation of the bottom dot plot is greater than that of the top dot plot.
b. A larger standard deviation means the tree heights at the farm represented by the bottom plot are more spread out from the mean height, while the tree heights at the farm represented by the top plot are more clustered around the mean.