Number of People You Have Known
Who Were Victims of Homicide
# of Victims Frequency
0 3944
1 279
2 97
3 40
4 30
Find the median. Note that the “4 or more” category is not problematic for it.
I know that the median is the middle number. I got 1.5 but book got 0. Please show me how they got 0. Not sure what I did wrong.
To find the median, you need to arrange the number of victims in ascending order.
The data provided is already sorted in ascending order, so you can directly find the median.
The total number of people known who were victims of homicide is:
0 * 3944 + 1 * 279 + 2 * 97 + 3 * 40 + 4 * 30 = 394 + 194 + 120 + 120 = 828
Since the total number of people known is even (828), the median will be the average of the two middle numbers.
To determine the position of the two middle numbers, you need to find the cumulative frequency that is closest to half the total frequency:
Half the total frequency = 828 / 2 = 414
From the data, we can see that the cumulative frequencies are:
0: 3944
1: 3944 + 279 = 4223
2: 4223 + 97 = 4320
3: 4320 + 40 = 4360
4: 4360 + 30 = 4390
The cumulative frequency closest to 414 is 4223. Therefore, the median will be in the "1" category, as it covers the closest cumulative frequency to 414.
Now we need to find the position of the median within the "1" category. Since the cumulative frequency of category 0 is 3944 and the cumulative frequency of category 1 is 4223, the median will be in the "1" category since it will fall within this range.
In the "1" category, the median will be the number that completes the cumulative frequency to half the total frequency, which is 414.
Since the "1" category corresponds to exactly 1 victim, the median will be 1.
Therefore, the median number of victims of homicide is 1.
To find the median, you need to sort the values in ascending order first.
In this case, we have the following categories and corresponding frequencies:
Number of Victims: 0 1 2 3 4 or more
Frequency: 3944 279 97 40 30
To calculate the median, we need to identify the middle point of the data set. Since there are 5330 total observations (sum of all frequencies), the middle point would be at the (5330 + 1) / 2 = 2665.5th observation.
To determine which category this observation falls into, we need to sum up the frequencies until we reach or exceed the 2665.5th observation.
Using this process:
- Cumulative Frequency of 0 = 3944 (This category is not included)
- Cumulative Frequency of 1 = 3944 + 279 = 4223 (This category is not included)
- Cumulative Frequency of 2 = 4223 + 97 = 4320 (This category is not included)
- Cumulative Frequency of 3 = 4320 + 40 = 4360 (This category is not included)
- Cumulative Frequency of 4 or more = 4360 + 30 = 4390 (This category is included)
Since the cumulative frequency of the "4 or more" category (4390) is greater than the middle point (2665.5), the median falls into this category.
To find the exact median value, we need to calculate the difference between the cumulative frequency at the start of the "4 or more" category (4360) and the middle point (2665.5).
The difference is: 4360 - 2665.5 = 1694.5.
Since this difference falls within the "4 or more" category, the median is 4 or more homicides (denoted by the category "4 or more").
Therefore, the book's answer of 0 seems incorrect, and the correct median value, according to the provided data, is 4 or more.