A company selling clothes on the internet reports that the package it ships have a median weight of 85 ounces with an IQR of 56 ounces. The company plans to include a sales flyer weighing 2 ounces in each package. what will the new median and IQR BE?
Median will increase 2 oz., but IQR will remain the same.
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To determine the new median and IQR, we need to take into account the additional weight of the sales flyer.
Given:
Original median weight = 85 ounces
Original IQR = 56 ounces
Weight of the sales flyer = 2 ounces
Step 1: Finding the new median
Since the sales flyer weighs 2 ounces, we need to add this weight to the original median.
New median = Original median + Weight of the sales flyer
New median = 85 ounces + 2 ounces
New median = 87 ounces
Step 2: Finding the new IQR
The IQR represents the range between the first quartile (Q1) and the third quartile (Q3). To determine the new IQR, we should adjust the weights of the quartiles.
Q1 = Median - (IQR / 2)
Q3 = Median + (IQR / 2)
Step 2.1: Updating Q1
New Q1 = New median - (Original IQR / 2)
New Q1 = 87 ounces - (56 ounces / 2)
New Q1 = 87 ounces - 28 ounces
New Q1 = 59 ounces
Step 2.2: Updating Q3
New Q3 = New median + (Original IQR / 2)
New Q3 = 87 ounces + (56 ounces / 2)
New Q3 = 87 ounces + 28 ounces
New Q3 = 115 ounces
Step 2.3: Calculating the new IQR
The new IQR is the difference between the new Q3 and the new Q1.
New IQR = New Q3 - New Q1
New IQR = 115 ounces - 59 ounces
New IQR = 56 ounces
In summary,
New median = 87 ounces
New IQR = 56 ounces
To find the new median and IQR, we need to consider the additional weight of the sales flyer.
1. Start with the median weight of the packages, which is given as 85 ounces. The median is the middle value when the data is arranged in ascending order.
2. Next, consider the IQR (Interquartile Range) of 56 ounces. The IQR is a measure of the spread of the middle 50% of the data. It is calculated as the difference between the third quartile (Q3) and the first quartile (Q1).
3. Since we know the IQR, we can calculate Q3 and Q1. Let's assume Q3 is the upper quartile, which is 56/2 = 28 ounces above the median. So, Q3 = 85 + 28 = 113 ounces. Similarly, assuming Q1 as the lower quartile, it will be 56/2 = 28 ounces below the median. So, Q1 = 85 - 28 = 57 ounces.
4. Now, add the weight of the sales flyer to each package. The flyer weighs 2 ounces, so the new weight of each package will be the original weight (median) plus 2 ounces.
5. Thus, the new median weight will be 85 + 2 = 87 ounces.
6. The new IQR will remain the same since the distribution of the data is not affected by adding a fixed value to each observation. Therefore, the new IQR will still be 56 ounces.
To summarize:
New Median: 87 ounces
New IQR: 56 ounces