Final answer:
From a histogram, you can estimate the mean by calculating the weighted midpoints of the intervals, and the median by identifying the interval containing the middle value. The mean, median, and mode coincide for symmetrical distributions but differ for skewed ones.
Step-by-step explanation:
Yes, it is possible to find the mean or median of a set of data from a histogram. The mean of a data set represents the central value by balancing the total quantity of the values. In the case of a histogram, the mean can be approximated by finding the midpoint of each interval, multiplying it by the frequency of that interval, summing these products across all intervals, and finally dividing by the total number of data values.
The median, which is the middle value that divides a data set into two equal halves, is a bit trickier to determine from a histogram, but it can be approximated. By arranging the data into intervals, you can determine which interval contains the middle value by adding the frequencies cumulatively until reaching the halfway point of the total number of observations. The median will be within that interval.
For skewed distributions, the mean is pulled towards the tail, whereas the median lies at the central position. For normal or symmetrical distributions, the mean, median, and mode coincide. However, for a skewed distribution, these measures of central tendency will differ. Looking at the shape of the histogram can give us insight into the relationship between these measures.