Class Interval for Continuous Data

Class interval = Upper Boundary -Lower Boundary

Using table 8, the class interval for the first class = 165-160 = 5

Class Midpoint for Continuous Data

Class Midpoint = Upper Boundary + Lower Boundary 2Using table 8, the class midpoint for the first class = 165+160 = 162.5 2

Mean for Ungrouped Frequency Distribution.

Question 1

Calculate the mean and express your answer in the following form:

a. two decimal plc

b.. in standard form

c. two Significant figure

X F FX

27 30 810

28 43 1204

29 51  

30 49  

31 42  

32 35  

Total 250  

Mean for Grouped Frequency Distribution:

X =

Where x is the midpoint of the classes.

On a certain day the number of books on 40 shelves in a library were noted and grouped as shown.

Question 2

Requirement

Calculate the mean to: (a) 3 significant figures

(b) 2 decimal places

Question 3

Calculate the mean to two decimal plc

Hieght Frequency160-165 7165-170 11170-175 17175-180 20180-185 16185-190 9

No. of Books X F (No. of Sheleves) FX31-35 33 4 132

36-40 38 6

41-45 43 10

46-50 48 13

51-55 53 5

56-60 58 2

Total   40

Median for Ungrouped Frequency Data

The steps for calculating the median for ungrouped data are as follows:

Steps

1. Calculate the cumulative frequency

2. Determine whether ∑ F is odd or even and apply the appropriate formula for the median

Example

X F Cumulative Frequency

27 30 0+30=30

28 43 30+43=73

29 51  

30 49  

31 42  

32 35  

Total 250  

Median =

Exercise 1

X F

1 32

2 25

3 18

4 14

5 11

Total 100

Find the median

Median for Grouped Frequency Data:

The steps for calculating the median for grouped data are as follows:

Steps

1. Determine if data is discrete or continuous .This is important in calculating the class interval. Remember, for discrete data the class interval = (upper boundary – lower boundary) +1 and for continuous the class interval = upper boundary – lower boundary

2. Calculate the cumulative frequency

3. Determine whether ∑ F is odd or even and apply the appropriate formula for ...the median class

4. using the )median class information, calculate the median

Example

Hieght Frequency Cumlative Frequency

160-165 7 7

165-170 11 18

170-175 17  

175-180 20  

180-185 16  

185-190 9  

Total 80  

Since n = 80

The median class =

Median formula : L + (n/2 -F)x i fm where L = lower limit of median class n = total frequency F= Cumulative frequency before the median class fm= Frequency of median class i = Class width of median class

median =

Example

No. of Books F (No. of Sheleves) Cumulative Frequency31-35 4 436-40 6 1041-45 10 2046-50 13 3351-55 5 3856-60 2 40Total 40  

Calculate the median.