What do you understand by the term mode of a data? Point out the methods of its computation in grouped and ungrouped data. Explain through examples.
Answers
Answer:
Grouped data is data that has been bundled together in categories. Histograms and frequency tables can be used to show this type of data:
Grouped Data vs. Ungrouped Data
Ungrouped data is the data you first gather from an experiment or study. The data is raw — that is, it’s not sorted into categories, classified, or otherwise grouped. An ungrouped set of data is basically a list of numbers.
When you have a frequency table or other group of data, the original set of data is lost — replaced with statistics for the group. You can’t find the exact sample mean (as you don’t have the original data) but you can find an estimate. The formula for estimating the sample mean for grouped data is:
mean for grouped dat
Answer:
The mode is the number that appears most frequently in a data set. A set of numbers may have one mode, more than one mode, or no mode at all. Other popular measures of central tendency include the mean, or the average (mean) of a set, and the median, the middle value in a set.
For ungrouped data:
Find the observation which occurs the maximum number of times
formula for ungrouped data
l+(f1-f0/2f1-f0-f2)
For grouped data:
Step 1. Find the maximum class frequency.
Step 2. Find the class corresponding to this frequency. It is called the modal class.
Step 3. Find the class size. (upper limit – lower limit.)
Step 4. Calculate mode using the formula.
formula for grouped data
l+f1-f0/2f1-f0-f2)
Example
A set of numbers consists of three 4s, five 5s, six 6s, eight 8s and seven 10s. The mode of this set of numbers is
(A) 6
(B) 7
(C) 8
(D) 10
Solution:
8 is represented 8 times. It comes maximum number of times. So, the mode is 8.
Hence option (c) is the answer.