Statistics
This chapter covers finding the mean, median, and mode of grouped data, and how to represent cumulative frequency data graphically using ogives.
Mean is the average value of a data set. Median is the middle value when data is arranged in order. Mode is the value that occurs most frequently. For grouped data, these are calculated using class marks and frequencies.
Mean = (sum of fi.xi) / (sum of fi), where xi is the class mark (midpoint) of each class interval and fi is the corresponding frequency. The class mark is calculated as (upper limit + lower limit) / 2.
Q. What is the class mark of the class interval 10-20?
Class mark = (upper limit + lower limit) / 2 = (20 + 10) / 2 = 30/2 = 15.
Empirical relationship between the three measures: Mode = 3(Median) - 2(Mean). This is useful when one measure is hard to calculate directly but the other two are known.
Q. Why is the median preferred over the mean when data has extreme values (outliers)?
The mean is affected by every value in the data set, so a very large or very small outlier can significantly distort it. The median, being a positional measure, is not affected by extreme values, making it a more reliable measure of central tendency for skewed data.
The graphical representation of cumulative frequency distribution is called a/an:
Correct answer: (B) Ogive
The value that appears most frequently in a data set is called the _______.
Mode
A data set can have more than one mode.
True — if two or more values occur with the same highest frequency, the data set is called bimodal (two modes) or multimodal (more than two modes).