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Jodi surveyed her friends about the number of calls they made over the weekend. The responses were 20, 23, 18, 4, 17, 21, 15, and 25. Use the range and interquartile range to describe how the data vary.

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Range: The range is the difference between the maximum and minimum values in a dataset.
To calculate the range:
Maximum value = 25
Minimum value = 4
Range = Maximum value - Minimum value =
25 - 4 = 21
Therefore, the range of the data is 21.
Interquartile range (IQR): The interquartile range is a measure of the spread of the data that focuses on the middle 50% of the dataset. It is calculated by subtracting the first quartile (Q1) from the third quartile (Q3).

To calculate the interquartile range:
First, we need to order the data from least to greatest: 4, 15, 17, 18, 20, 21, 23, 25
The median is the middle value, which is the average of the two middle values in this
case: (18 + 20) / 2 = 19
Q1 is the median of the lower half of the data, which is the middle value of the first
half: (15 + 17) / 2 = 16
Q3 is the median of the upper half of the data, which is the middle value of the
second half: (21 + 23) / 2 = 22
To calculate the interquartile range:
IQR = Q3 - Q1 = 22 - 16 = 6
Therefore, the interquartile range of the data is 6.

Now, let's describe how the data vary using the range and interquartile range:
The range of 21 shows that the data vary quite a bit, with the maximum value being 21 units greater than the minimum value.
The interquartile range of 6 indicates that the middle 50% of the data is relatively tightly clustered, with the spread between the first and third quartiles being 6 units.
Overall, the data exhibit a wide range of values, but the bulk of the data is relatively close together.
User Viswanath Polaki
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