The 50 percentile is equivalent to the median or the second quartile.
Further Explanation
In Statistics, studying about the measures of central tendency and measures of position play an important role. The measures of central tendency can represent huge data, for example, a mean or an average can be a good estimation to represent very huge data. The measures position can tell us if the value is lower or above the average or mean.
Measures of Central Tendency
1. The mean or the average
2. The median
3. The mode
Common Measures of Position
1. Quartiles
2. Deciles
3. Percentiles
The median is the middle point of the data set after the data is arranged in either ascending order or descending order.
The percentile divides the data set into 100 equal parts, thus there are 99 position values available. As you can see, the 50th percentile is actually the 50th percent rank which is the middle point of the data set.
Let's have this data as an example:
25, 34, 47, 12, 45, 28
To solve for the median, arrange the data set in ascending order and then pick the middle value.
Ascending Order:
12, 25, 28, 34, 47
It's clear in the arrangement that the median or the middle value is 28.
Now, to solve for the 50th percentile use the formula where n is the total number of observations, in this case, it's 5, and is the percentile value, in this case, it's 50.
Substitute the values of and into the formula, then simplify the right side.
This means that the 3rd value that you can see on the arranged data is the 50th percentile, which is 28.
The process above confirms that the 50th percentile is equivalent to the median.
Answers & Comments
Answer:
The 50th percentile is generally the median; it is commonly assumed that 50% the values in a data set are above the median.
Answer:
The 50 percentile is equivalent to the median or the second quartile.
Further Explanation
In Statistics, studying about the measures of central tendency and measures of position play an important role. The measures of central tendency can represent huge data, for example, a mean or an average can be a good estimation to represent very huge data. The measures position can tell us if the value is lower or above the average or mean.
Measures of Central Tendency
1. The mean or the average
2. The median
3. The mode
Common Measures of Position
1. Quartiles
2. Deciles
3. Percentiles
The median is the middle point of the data set after the data is arranged in either ascending order or descending order.
The percentile divides the data set into 100 equal parts, thus there are 99 position values available. As you can see, the 50th percentile is actually the 50th percent rank which is the middle point of the data set.
Let's have this data as an example:
25, 34, 47, 12, 45, 28
To solve for the median, arrange the data set in ascending order and then pick the middle value.
Ascending Order:
12, 25, 28, 34, 47
It's clear in the arrangement that the median or the middle value is 28.
Now, to solve for the 50th percentile use the formula where n is the total number of observations, in this case, it's 5, and is the percentile value, in this case, it's 50.
Substitute the values of and into the formula, then simplify the right side.
This means that the 3rd value that you can see on the arranged data is the 50th percentile, which is 28.
The process above confirms that the 50th percentile is equivalent to the median.
Step-by-step explanation: