1. Raquel is enrolled in a computer course and one of the assignments is typing speed. She keeps track of the number of words she types in each minute. The results are shown in the table.
32 30 34 27 28 30
29 31 33 36 26 31
Explain whether the five-number summary shown below represents the data.
minimum: 26 first quartile: 27; median: 31 third quartile: 33 maximum: 36
A. The five-number summary shown is incorrect. The first quartile is actually 28.5, the median is 30.5, and the third quartile is 32.5.
B. The five-number summary shown is incorrect. The median is actually 30
and the maximum is 34
C. The five-number summary shown is incorrect. The minimum is actually 27 and the third quartile is 32
D. The five-number summary shown is incorrect. The first quartile is actually 27.5, the median is 31.5, and the third quartile is 33.5
2. An online retailer has two warehouses, M and N, where customers' orders are packaged and shipped. The number of orders per day for warehouse M has a mean of 1,417.31 and a standard deviation of 67.54. The mean number of orders per day is 1,505.39 for warehouse N with a standard deviation of 67.70. Explain how the number of orders per day for warehouse M compare to the number of order per day for warehouse N.(1 point)
A. The number of orders per day for warehouse M is about the same on average to the number of orders per day for warehouse N. The standard deviation for the number of orders per day in warehouse M is greater than the standard deviation for warehouse N.
B. The number of orders per day for warehouse N is greater on average than the number of orders per day for warehouse M. The standard deviation for the number of orders per day in warehouse N is about the same as in warehouse M.
C. The number of orders per day for warehouse N is less on average than the number of orders per day for warehouse M. The standard deviation for the number of orders per day in warehouse N is greater than the standard deviation in warehouse M.
D. The number of orders per day for warehouse M is greater on average than the number of orders per day for warehouse N. The standard deviation for the number of orders per day in warehouse N is about the same as in warehouse M.
1. D. The five-number summary shown is incorrect. The first quartile is actually 27.5, the median is 31.5, and the third quartile is 33.5. (This can be determined by sorting the data and finding the median, which is the middle value. The first quartile is the median of the lower half of the data, and the third quartile is the median of the upper half of the data.)
2. B. The number of orders per day for warehouse N is greater on average than the number of orders per day for warehouse M. The standard deviation for the number of orders per day in warehouse N is about the same as in warehouse M. (This can be determined by comparing the means of the two warehouses, which shows that N has a higher average number of orders per day. The standard deviations can also be compared, which shows that they are very similar.)
1. The correct answer is D. The five-number summary shown is incorrect. The first quartile is actually 27.5, the median is 31.5, and the third quartile is 33.5. The minimum is 26 and the maximum is 36.
2. The correct answer is A. The number of orders per day for warehouse M is about the same on average as the number of orders per day for warehouse N. However, the standard deviation for the number of orders per day in warehouse M is greater than the standard deviation for warehouse N.
1. To determine if the five-number summary represents the data in the given table, we first need to understand what the five-number summary represents. The five-number summary consists of the minimum, first quartile, median, third quartile, and maximum of a dataset.
Looking at the given data (32 30 34 27 28 30 29 31 33 36 26 31), we can sort it in ascending order: 26 27 28 29 30 30 31 31 33 34 36.
The minimum value is clearly 26, so the first part of the five-number summary is accurate.
To find the first quartile, we divide the data into four equal parts. Since the data has 12 values, the first quartile would be at the position (12+1)/4 = 3.25. This means we take the average of the 3rd and 4th values, which gives us (28 + 29)/2 = 28.5. Therefore, the correct value for the first quartile is 28.5.
The median is the middle value in the data. Since we have an even number of data points, the median would be the average of the two middle values. In this case, the two middle values are 30 and 30, so the median is (30 + 30)/2 = 30. Therefore, the median value is correct in the given five-number summary.
For the third quartile, we multiply the position by 3, so (12+1)*3/4 = 9.75. This means we take the average of the 9th and 10th values, which gives us (33 + 34)/2 = 33.5. Therefore, the correct value for the third quartile is 33.5.
Finally, the maximum value is clearly 36, so the last part of the five-number summary is accurate.
Putting it all together, the correct five-number summary for the given data is:
minimum: 26, first quartile: 28.5, median: 30, third quartile: 33.5, maximum: 36.
Therefore, the correct answer is D. The five-number summary shown is incorrect. The first quartile is actually 27.5, the median is 31.5, and the third quartile is 33.5.
2. To compare the number of orders per day for warehouse M and warehouse N, we need to consider the mean and standard deviation of the two datasets.
The mean number of orders per day for warehouse M is 1,417.31, while the mean number of orders per day for warehouse N is 1,505.39. This means that, on average, warehouse N receives a greater number of orders per day compared to warehouse M.
The standard deviation for warehouse M is 67.54, while the standard deviation for warehouse N is 67.70. The standard deviation measures the variability or spread of the data. In this case, the standard deviation for both warehouses is quite similar, with warehouse N having a slightly larger standard deviation.
Therefore, the correct answer is D. The number of orders per day for warehouse M is greater on average than the number of orders per day for warehouse N. The standard deviation for the number of orders per day in warehouse N is about the same as in warehouse M.