Question

1. a mathematics teacher marked a set of 30 exam papers. the grades are displayed below: 90,85,74,86,65,62,95,77,82,50,83,77,93,73,72 98,66,45,50,89,78,70,75,95,80,78,83,81,72,75 (a) complete the table below: interval tally frequency class mark relative frequency cumulative frequency 40 - 50 50 - 60 60 - 70 70 - 80 80 - 90 90 - 100 (b) what is the class width?

Explanation:

Step1: Recall class - width formula

Class width = Upper - class limit - Lower - class limit

Step2: Take an interval example

For the interval 40 - 50, upper - class limit = 50, lower - class limit = 40

Step3: Calculate class width

Class width=50 - 40 = 10. This is the same for all intervals (e.g., for 50 - 60: 60 - 50 = 10; for 60 - 70: 70 - 60 = 10, etc.).

(a)

Interval	Tally	Frequency	Class Mark	Relative Frequency	Cumulative Frequency
50 - 60	//// ////	8	55	$\frac{8}{30}\approx0.267$	4 + 8=12
60 - 70	//// ////	8	65	$\frac{8}{30}\approx0.267$	12+8 = 20
70 - 80	//// ////	8	75	$\frac{8}{30}\approx0.267$	20 + 8=28
80 - 90	/	1	85	$\frac{1}{30}\approx0.033$	28+1 = 29
90 - 100	/	1	95	$\frac{1}{30}\approx0.033$	29 + 1=30

for (a):

Step1: Count tallies

Go through the data set and count the number of values that fall into each interval to get the frequency. For example, for the 40 - 50 interval, count how many scores are between 40 and 50.

Step2: Calculate class mark

Class mark = $\frac{\text{Lower - class limit}+\text{Upper - class limit}}{2}$, e.g., for 40 - 50, $\frac{40 + 50}{2}=45$.

Step3: Calculate relative frequency

Relative frequency = $\frac{\text{Frequency}}{\text{Total number of data points}}$, here the total number of data points is 30.

Step4: Calculate cumulative frequency

Cumulative frequency for an interval is the sum of the frequencies of that interval and all previous intervals.

Answer:

(b) 10