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The stem-and-leaf plot shows the heights in centimeters of Teddy Bear sunflowers grown in two different types of soil.
Soil A Soil B
5 9
5 2 1 1 6 3 9
5 1 0 7 0 2 3 6 7 8
2 1 8 3
0 9
Key: 9|6 means 69 Key: 5|8 means 58
Calculate the mean of each data set.
Calculate the mean absolute deviation (MAD) of each data set.
Which set is more variable? How do you know?
I'm sorry, but I cannot see the stem-and-leaf plot or the space provided to enter the answer and show steps. Can you please provide me with this information so that I can help you with the math question?
Soil A Soil B
5 9
5 2 1 1 6 3 9
5 1 0 7 0 2 3 6 7 8
2 1 8 3
0 9
Key: 9|6 means 69 Key: 5|8 means 58
a. The overlap is the range of data that is common to both soils, namely between 61 (from soil A) and 83 (from soil B).
b. The mean is the average, calculated by adding up all data and dividing the sum by the number of values.
Soil A:
(61+61+62+65+70+71+75+81+82+90)/10=71.8
c. the mean absolute deviation (MAD) is also called the mean deviation. This is obtained by adding the difference between each value and the mean, but without regard to the sign. The sum is then divided again by the number of values.
MAD for soil A
= ((71.8-61)+(71.8-61)+(71.8-62)+...
+(71.8-71)+(75-71.8)+(81-71.8)+(82-71.8)+(90-71.8))/10
=8.16
d. compare the size of MAD for each soil.
MAD measures the variability of a dataset.
From the calculations, we can see that the MAD for Soil A is 8.16 and the MAD for Soil B cannot be calculated as the data is not provided. However, we can conclude that Soil A is more variable than Soil B as the MAD for Soil A is relatively higher.
Which question is a statistical question?
Responses
A Does my father or my mother like the ice-cream from the grocery store better?Does my father or my mother like the ice-cream from the grocery store better?
B How do I rate the taste of ice-cream on a scale of 1-10?How do I rate the taste of ice-cream on a scale of 1-10?
C How does my brother rate the taste of ice-cream on a scale of 1-10?How does my brother rate the taste of ice-cream on a scale of 1-10?
D Which brand of ice cream is preferred by the people shopping at a grocery store?
D Which brand of ice cream is preferred by the people shopping at a grocery store? is a statistical question.
Thank you for providing the stem-and-leaf plot.
To calculate the mean of Soil A:
- Count the number of data points in Soil A: 14
- Add up all the heights in Soil A: 521 + 536 + 510 + 281 + 90 = 1938
- Divide the sum by the number of data points: 1938 / 14 = 138.43
Therefore, the mean of Soil A is 138.43 cm.
To calculate the mean of Soil B:
- Count the number of data points in Soil B: 20
- Add up all the heights in Soil B: 693 + 369 + 723 + 831 = 2616
- Divide the sum by the number of data points: 2616 / 20 = 130.8
Therefore, the mean of Soil B is 130.8 cm.
To calculate the mean absolute deviation (MAD) of Soil A:
- Find the absolute deviation for each data point by subtracting the mean from the data point and taking the absolute value:
- for 521, |521 - 138.43| = 382.57
- for 536, |536 - 138.43| = 397.57
- for 510, |510 - 138.43| = 371.57
- for 281, |281 - 138.43| = 142.57
- for 90, |90 - 138.43| = 48.43
- for 521, |521 - 138.43| = 382.57
- for 536, |536 - 138.43| = 397.57
- for 510, |510 - 138.43| = 371.57
- for 281, |281 - 138.43| = 142.57
- for 90, |90 - 138.43| = 48.43
- for 291, |291 - 138.43| = 152.57
- for 380, |380 - 138.43| = 241.57
- for 238, |238 - 138.43| = 99.57
- for 309, |309 - 138.43| = 170.57
- Add up all the absolute deviations: 382.57 + 397.57 + 371.57 + 142.57 + 48.43 + 382.57 + 397.57 + 371.57 + 142.57 + 48.43 + 152.57 + 241.57 + 99.57 + 170.57 = 2850.47
- Divide the sum by the number of data points: 2850.47 / 14 = 203.6
Therefore, the MAD of Soil A is 203.6 cm.
To calculate the mean absolute deviation (MAD) of Soil B:
- Find the absolute deviation for each data point by subtracting the mean from the data point and taking the absolute value:
- for 569, |569 - 130.8| = 438.2
- for 638, |638 - 130.8| = 507.2
- for 339, |339 - 130.8| = 208.2
- for 238, |238 - 130.8| = 107.2
- for 783, |783 - 130.8| = 652.2
- for 301, |301 - 130.8| = 170.2
- for 672, |672 - 130.8| = 541.2
- for 239, |239 - 130.8| = 108.2
- for 363, |363 - 130.8| = 232.2
- for 180, |180 - 130.8| = 49.2
- for 237, |237 - 130.8| = 106.2
- for 367, |367 - 130.8| = 236.2
- for 758, |758 - 130.8| = 627.2
- for 938, |938 - 130.8| = 807.2
- Add up all the absolute deviations: 438.2 + 507.2 + 208.2 + 107.2 + 652.2 + 170.2 + 541.2 + 108.2 + 232.2 + 49.2 + 106.2 + 236.2 + 627.2 + 807.2 = 4953.6
- Divide the sum by the number of data points: 4953.6 / 20 = 247.68
Therefore, the MAD of Soil B is 247.68 cm.
To determine which set is more variable:
- Compare the MAD values for Soil A (203.6) and Soil B (247.68).
- The set with the larger MAD is more variable.
- In this case, Soil B has a larger MAD, so it is more variable.
- This means that the heights of the Teddy Bear sunflowers grown in Soil B have more variation or are more spread out than the heights of the sunflowers grown in Soil A.
Rainfall Data
Month Rainfall (cm)
January 4.3
February 3.9
March 4.0
April 5.0
May 2.9
June 3.2
July 1.9
August 2.0
September 3.7
October 3.8
November 4.2
December 4.9
What is the mode of the data in the rainfall table?
Responses
A 3.13.1
B 3.653.65
C no modeno mode
D 5.05.0
E 3.73.7
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