The dot plots below show the number of pairs of shoes sold at two stores each day during November. What is the difference of the medians as a multiple of the interquartile range?
the numbers for pairs of shoes sold for store one are 16 18 20 22 24 26 28 30 and 32 and the dots for each one are none for 16 4 for 18 2 for 20 4 for 22 3 for 24 4 for 26 7 for 28 1 for 30 and 5 for 32
store 2's numbers are 22 24 28 30 32 34 36 38 dots for each number are as follow 1 for 22 and 1 for 24 4 for 26 and for 28 aswell 5 for 30 6 for 32 4 for 34 3 for 36 and 2 for 38
First, we need to find the medians and interquartile ranges for each store.
For store 1:
- Median = 24
- Q1 (first quartile) = 20
- Q3 (third quartile) = 28
- IQR (interquartile range) = Q3 - Q1 = 8
For store 2:
- Median = 32
- Q1 = 28
- Q3 = 36
- IQR = 8
The difference of the medians is:
32 - 24 = 8
And as a multiple of the IQR:
8 รท 8 = 1
Therefore, the difference of the medians as a multiple of the IQR is 1.
To find the difference of the medians as a multiple of the interquartile range, let's first calculate the medians for both stores.
For Store 1:
The median is the middle value of the data set when arranged in ascending order. Since there are 9 values, the median will be the 5th value.
Arranging the numbers in ascending order: 16, 18, 20, 22, 24, 26, 28, 30, 32
The median is the 5th value, which is 24.
For Store 2:
Similarly, the median is the middle value of the data set when arranged in ascending order. Since there are 8 values, the median will be the 4th value.
Arranging the numbers in ascending order: 22, 24, 26, 28, 30, 32, 34, 36, 38
The median is the 4th value, which is 28.
Now, let's calculate the interquartile range for both stores.
For Store 1:
The interquartile range is the difference between the third quartile (Q3) and the first quartile (Q1).
Q3 is the median of the upper half of the data set, and Q1 is the median of the lower half.
Arranging the numbers in ascending order: 16, 18, 20, 22, 24, 26, 28, 30, 32
The lower half is: 16, 18, 20, 22
The upper half is: 26, 28, 30, 32
Q1 is the median of the lower half, which is 19 (the average of 18 and 20).
Q3 is the median of the upper half, which is 29 (the average of 28 and 30).
The interquartile range (IQR) = Q3 - Q1 = 29 - 19 = 10.
For Store 2:
Arranging the numbers in ascending order: 22, 24, 26, 28, 30, 32, 34, 36, 38
The lower half is: 22, 24, 26, 28
The upper half is: 30, 32, 34, 36
Q1 is the median of the lower half, which is 25 (the average of 24 and 26).
Q3 is the median of the upper half, which is 33 (the average of 32 and 34).
The interquartile range (IQR) = Q3 - Q1 = 33 - 25 = 8.
Now, we can calculate the difference of the medians as a multiple of the interquartile range.
Difference of medians = 28 - 24 = 4
Difference of medians as a multiple of the interquartile range = 4 / 10 = 0.4
Therefore, the difference of the medians as a multiple of the interquartile range is 0.4.