Question
The data shows the number of seconds it took two randomly selected groups to thread a needle. Compare the measures of center and variability of these data sets.
Student Group A: 56, 14, 26, 28, 29, 45, 32, 80, 3, 10
Student Group B: 27, 24, 18, 19, 5, 16, 22, 10, 6, 20
Which of the following statements about these data sets is false?
(1 point)
Responses
The ranges of the time taken by Group A and Group B are the same.
The ranges of the time taken by Group A and Group B are the same.
The mean time taken by Group A is higher than that of Group B.
The mean time taken by Group A is higher than that of Group B.
The amount of variability of the time taken by Group A to thread a needle is higher than the amount of variability of the time taken by Group B.
The amount of variability of the time taken by Group A to thread a needle is higher than the amount of variability of the time taken by Group B.
The median time taken by members of Group A to thread a needle is higher than that of members of Group B.
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The statement "The ranges of the time taken by Group A and Group B are the same" is false.
Two fertilizer are applied to randomly selected potatoes are weighted.the weights in kilograms are as follows.which fertilizer is generally more effective?
Fertilizer A: 27,20,16,18,22,19,23,21,17,19
Fertilizer B: 28,19,18,21,24,20,25,27,29,21
To determine which fertilizer is generally more effective, we can compare the measures of center and variability of the weights for potatoes treated with each fertilizer.
Measures of center:
- Fertilizer A: mean = 20.2, median = 19.5
- Fertilizer B: mean = 22.2, median = 21.5
Measures of variability:
- Fertilizer A: range = 11, interquartile range = 4, standard deviation = 3.34
- Fertilizer B: range = 11, interquartile range = 4.5, standard deviation = 3.56
Based on these measures, we can see that Fertilizer B has a slightly higher mean and median weight for potatoes, indicating that it may be more effective. However, the measures of variability for both fertilizers are fairly similar, with Fertilizer A having a slightly smaller interquartile range and standard deviation.
Overall, it's difficult to definitively say which fertilizer is generally more effective based on these measures alone. Additional analysis, such as hypothesis testing or confidence intervals, may be needed to make a more conclusive determination.
To compare the measures of center and variability between the two data sets (Student Group A and Student Group B), we can look at different statistics.
1. Range: The range is the difference between the maximum and minimum values in a data set. To calculate the range, we find the maximum value and subtract the minimum value.
For Group A: Maximum = 80, Minimum = 3 → Range = 80 - 3 = 77
For Group B: Maximum = 27, Minimum = 5 → Range = 27 - 5 = 22
Therefore, the statement "The ranges of the time taken by Group A and Group B are the same" is FALSE. The range of Group A is higher than the range of Group B.
2. Mean: The mean is the average of the values in a data set. To calculate the mean, we sum up all the values and divide by the total number of values.
For Group A: Mean = (56 + 14 + 26 + 28 + 29 + 45 + 32 + 80 + 3 + 10) / 10 = 31.3
For Group B: Mean = (27 + 24 + 18 + 19 + 5 + 16 + 22 + 10 + 6 + 20) / 10 = 16.7
Therefore, the statement "The mean time taken by Group A is higher than that of Group B" is TRUE. The mean of Group A is higher than the mean of Group B.
3. Variability: Variability measures how spread out the data values are. One common measure of variability is the standard deviation. However, to compare the variability in this case, we can look at the range (already calculated) and the median.
For Group A, previously calculated range = 77,
Median = the middle value (when arranged in ascending order) = 28.0
For Group B, previously calculated range = 22,
Median = the middle value (when arranged in ascending order) = 17.0
Therefore, the statement "The amount of variability of the time taken by Group A to thread a needle is higher than the amount of variability of the time taken by Group B" is TRUE. The range and median of Group A indicate higher variability compared to Group B.
4. Median: The median is the middle value when the data set is arranged in ascending order.
Therefore, the statement "The median time taken by members of Group A to thread a needle is higher than that of members of Group B" is FALSE. The median of Group A is lower than the median of Group B.
In summary, the false statement is: "The median time taken by members of Group A to thread a needle is higher than that of members of Group B."