The standard deviation of a data set is 4. What is the variance?
(1 point)
Responses
2
2
4
4
8
8
16
The correct answer is 16.
City 2010 2011 2012 2013 2014 2015
Seattle, WA 45.79 32.46 55.14 40.30 23.78 49.42
Las Vegas, NV 3.72 5.62 4.11 8.79 2.33 3.84
What is the difference between the median yearly rainfall for Seattle and Las Vegas?
(1 point)
Responses
36.58 in.
36.58 in.
39.07 in.
39.07 in.
41.68 in.
41.68 in.
43.045 in.
43.045 in.
To find the median yearly rainfall for each city, we first need to arrange the rainfall data in ascending order:
Seattle, WA: 23.78, 32.46, 40.30, 45.79, 49.42, 55.14
Las Vegas, NV: 2.33, 3.72, 3.84, 4.11, 5.62, 8.79
Since there is an even number of data points for each city, we take the average of the middle two values to find the median:
Median rainfall for Seattle = (40.30 + 45.79)/2 = 43.045 in.
Median rainfall for Las Vegas = (3.84 + 4.11)/2 = 3.975 in.
The difference between the median yearly rainfall for Seattle and Las Vegas is 43.045 - 3.975 = 39.07 in.
Therefore, the correct answer is 39.07 in.
Which data set has the same range as the box-and-whisker plot shown?
A box and whisker plot is shown. A number line graph with a green rectangle extending from 5 to 9.5 above the line. There is a green dot at each end of the rectangle. There is a vertical line inside the rectangle at 8 with a red dot on it. There are black dots to the right and left of the green rectangle at 4 and 10. These black dots are connected to the green dots at their end of the green rectangle with black line segments.
(1 point)
Responses
14, 26, 32, 20
14, 26, 32, 20
64, 60, 62, 63, 63, 65
64, 60, 62, 63, 63, 65
19, 16, 26, 18, 23
19, 16, 26, 18, 23
11, 9, 15, 14, 9, 12
To determine which data set has the same range as the given box-and-whisker plot, we need to find the difference between the minimum and maximum values of the plot.
From the box-and-whisker plot, we can see that the minimum value is approximately 4 and the maximum value is approximately 10.
We can now compare these values to the range of each given data set:
1) Range of data set 14, 26, 32, 20 = 32 - 14 = 18
2) Range of data set 64, 60, 62, 63, 63, 65 = 65 - 60 = 5
3) Range of data set 19, 16, 26, 18, 23 = 26 - 16 = 10
4) Range of data set 11, 9, 15, 14, 9, 12 = 15 - 9 = 6
Based on the range values, the only data set that has the same range as the given box-and-whisker plot (approximately 4 to 10) is:
19, 16, 26, 18, 23
Therefore, the correct answer is 19, 16, 26, 18, 23.
The variance of a data set is 4. What is the standard deviation?
(1 point)
Responses
2
2
4
4
8
8
16
The standard deviation of a data set is the square root of the variance. In this case, if the variance is 4, then the standard deviation would be the square root of 4, which is 2.
Therefore, the correct answer is 2.
Calculate the interquartile range of the data set.
{37, 46, 32, 40, 33, 40, 36, 30}
(1 point)
Responses
8
8
7.5
7.5
7
7
6.5
To calculate the interquartile range (IQR) of a data set, we first need to find the first quartile (Q1) and the third quartile (Q3).
To do this, we first need to arrange the data set in ascending order:
{30, 32, 33, 36, 37, 40, 40, 46}
Next, we can find Q1 and Q3 using the formulas:
Q1 = (n + 1) / 4
Q3 = 3(n + 1) / 4
where n is the number of data points. In this case, n = 8.
Q1 = (8 + 1) / 4 = 2.25
Q3 = 3(8 + 1) / 4 = 6.75
Finally, we can calculate the IQR by subtracting Q1 from Q3:
IQR = Q3 - Q1 = 6.75 - 2.25 = 4.5
Therefore, the correct answer is 4.5.