Mark scored by $20$ students in a mathematics test are given as follows:
$60, 65, 70, 60, 75, 55, 70, 65, 55, 80, 50, 75, 80, 60, 70, 75, 55, 60, 80, 55$
Prepare a frequency table.

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Solution

Step 1: To prepare a frequency table, create a column for marks obtained by students and then tally the numbers in tally marks column.
Marks
Tally Marks
50
I
55
IIII
60
IIII
65
II
70
III
75
III
80
III
Step 2: Count the tally marks and note down the frequency in the frequency column.
Marks
Tally Marks
Frequency
50
I
1
55
IIII
4
60
IIII
4
65
II
2
70
III
3
75
III
3
80
III
3

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8(ii) State the modal Class

Class Interval	$50 - 55$	$55 - 60$	$60 - 65$	$65 - 70$	$70 - 75$	$75 - 80$	$80 - 85$	$85 - 90$
Frequency	$5$	$20$	$10$	$10$	$9$	$6$	$12$	$8$

The weight (in grams) of $40$ oranges picked at random from a basket are as follows:

$50, 40, 60, 65, 45, 55, 30, 90, 75, 85, 70, 85, 75, 80, 100, 110, 70, 55, 30, 35, 45, 70, 80, 85, 95, 70, 60, 70, 75, 40, 100, 65, 60, 40, 100, 75, 110, 30, 84, 45 .$

Construct a frequency table as well as a cumulative frequency table.

8.(i) Using step-deviation method, calculate the mean marks of the following distribution.

Class Interval	$50 - 55$	$55 - 60$	$60 - 65$	$65 - 70$	$70 - 75$	$75 - 80$	$80 - 85$	$85 - 90$
Frequency	$5$	$20$	$10$	$10$	$9$	$6$	$12$	$8$

The following table gives the weekly wages of workers in a factory

Weekly Wages	$50 - 55$	$55 - 60$	$60 - 65$	$65 - 70$	$70 - 75$	$75 - 80$	$80 - 85$	$85 - 90$
No. of workers	$5$	$20$	$10$	$10$	$9$	$6$	$12$	$8$

Calculate

(i) the mean

Q. Estimate the median for the following data given below

:

Marks	$50 - 55$	$55 - 60$	$60 - 65$	$65 - 70$	$70 - 75$
Students	$50$	$40$	$30$	$20$	$10$

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Marks	Tally Marks	Frequency
50	I	1
55	IIII	4
60	IIII	4
65	II	2
70	III	3
75	III	3
80	III	3

Mark scored by 20 students in a mathematics test are given as follows:60,65,70,60,75,55,70,65,55,80,50,75,80,60,70,75,55,60,80,55Prepare a frequency table.

Mark scored by $20$ students in a mathematics test are given as follows:
$60, 65, 70, 60, 75, 55, 70, 65, 55, 80, 50, 75, 80, 60, 70, 75, 55, 60, 80, 55$
Prepare a frequency table.