when calculating the median from a frequency table, do you do (the total+1)/2 or just the total/2?
When calculating the median from a frequency table, you do (the total+1)/2.
because everywhere i check they say different things smh
I apologize for the confusion. Whether to use (total/2) or (total+1)/2 when calculating the median from a frequency table can depend on the context or the specific method being used to calculate the median.
One common method for finding the median from a frequency table is to simply find the middle value of the data set (by adding the frequencies until you reach the middle value), and then finding the corresponding value in the data set. In this case, (total+1)/2 would be used if there is an odd number of values, and (total/2) would be used if there is an even number of values.
However, some other methods of finding the median from a frequency table may use different formulas or adjustments. It's always important to check the context and instructions carefully to determine the correct method to use.
ohhh
so if it comes a decimal when you just /2, you have to +1 then /2?
Yes, that's correct. If you end up with a decimal value when dividing the total by 2, you would need to add 1 to the result before dividing by 2 to find the median.
For example, let's say you have a frequency table with a total of 25 values. When you divide 25 by 2, you get 12.5. Since 12.5 is not a whole number, you would add 1 to get 13, and then divide by 2 to get the median value.
The table shows some information about the dress sizes of 25 women.
(a) Find the median dress size.
3 of the 25 women have a shoe size of 7
Zoe says that if you choose at random one of the 25 women, the probability that she has either a shoe size of 7 or a dress size of 14 is 9/25
because
3/25 + 6/25 = 9/25
(b) Is Zoe correct?
You must give a reason for your answer.
(a) To find the median dress size from the table, we need to first arrange the data in ascending order:
Dress Size | Frequency
--------- | ---------
8 | 3
10 | 5
12 | 9
14 | 5
16 | 3
The total number of women is 25. The median is the middle value of the data set, so we can find it by adding up the frequencies until we reach the middle value (which is 13 in this case). The 13th value falls into the "12" dress size category, so the median dress size is 12.
(b) Zoe is incorrect. The probability that a woman chosen at random has either a shoe size of 7 or a dress size of 14 cannot be found simply by adding the probabilities of those two events separately. This is because the events are not mutually exclusive. Some women in the sample may have both a shoe size of 7 and a dress size of 14.
To find the correct probability, we can use the formula:
P(Shoe size 7 or Dress size 14) = P(Shoe size 7) + P(Dress size 14) - P(Shoe size 7 and Dress size 14)
From the table, we know that 3 women have a shoe size of 7 and 5 women have a dress size of 14. We don't know how many women have both, but we know that the total number of women is 25, so the maximum number of women that could have both is 3 (the number of women with a shoe size of 7).
Therefore, the probability that a woman chosen at random has either a shoe size of 7 or a dress size of 14 is:
P(Shoe size 7 or Dress size 14) = 3/25 + 5/25 - 3/25 = 5/25 = 1/5
So Zoe's calculation is not correct because it doesn't account for the possibility of some women having both a shoe size of 7 and a dress size of 14.