To find the mean, add up all the numbers and divide by the number of numbers • To find the median, following frequency distribution was obtained
Example 2 15 Find the mean deviation from the A M for the following distribution Class interval 10–20 20–30 30–40 40–50 50–60 Frequency
Example: The following table gives the frequency distribution of the number of orders received each day during the past 50 days at the office of a mail-order
The following frequency distribution of marks has mean 4 5 (a) Calculate an estimate for the standard deviation of the lengths of the fish
Long Answer Type Example 5 Calculate mean, variation and standard deviation of the following frequency distribution: Classes Frequency
The mean for grouped data is obtained from the following formula: Given the following frequency distribution, calculate the arithmetic mean Marks : 64
n = total frequency c = width of the class interval Example 2 Given the following frequency distribution, calculate the arithmetic mean
Find the class width: Determine the range of the data and divide this by the Make a frequency distribution for the following data, using 5 classes:
condensation of data set into a frequency distribution and visual presentation are Calculate the arithmetic mean for the following data given below:
For finding the mean of grouped data di's are deviations from a of (A) Lower limits of the classes Consider the following frequency distribution:
the class. Each class will have a \lower class limit" and an \upper class limit" which are the lowest
and highest numbers in each class. The \class width" is the distance between the lower limits of consecutive classes. Therangeis the dierence between the maximum and minimum data entries. Steps for constructing a frequency distribution from a data set 1. If the n umberof classes i snot giv en,decide on a n umberof classes to use. T hisn umbershould be between 5 and 20. 2. Find the class w idth:Determine th erange of the d ataand divide this b ythe n umberof classes. Round up to the next convenient number (if it's a whole number, also round up to the next whole number). 3. Find the class limits: Y oucan use the minim umd ataen tryas the lo werlimit of th erst class. To get the lower limit of the next class, add the class width. Continue until you reach the last class. Then nd the upper limits of each class (since the classes cannot overlap, and occasionally your data will include decimal numbers, remember that it's ne for the upper limits to be decimals). 4. Coun tthe n umberof data en triesfor eac hclass, and record the n umberin the ro wof the table for that class. (The book recommends using \tally" marks to count)The smallest number is 5, and the largest is 25, so the range is 20. The class width will be 20=5 = 4,
but we need to round up, so we will use 5. Our classes will be 5{9, 10{14, 15{19, 20{24, and 25{29. Then, counting the number of entries in each class, we get:ClassFrequency 5{910The \relative frequency" of each class is the proportion of the data that falls in that class. It can
be calculated for a data set of sizenby: