Marks obtained by 50 students in a test of 50 marks are as follow… - Vidyadip

Question

Marks obtained by $50$ students in a test of $50$ marks are as follows :
$\text{16 18 27 31 43 25 28 30 29 15}$
$\text{20 27 31 34 39 41 22 28 31 16}$
$\text{21 29 38 24 30 24 26 17 30 22}$
$\text{28 35 23 18 24 32 37 27 32 38}$
$\text{19 25 33 25 29 25 34 45 26 24}$
$(i)$ From these data, prepare a frequency distribution by taking class length $5$ .
$(ii)$ Obtain 'less than' and 'more than' type cumulative frequency distribution.
$(iii)$ If standard of passing is $20$ marks, then how many students have failed ?
$(iv)$ If at least $30$ marks are required to get first class, find the number of students in this category.

✓

Answer

$(i)$ Frequency distribution of marks obtained by students in a test of $50$ marks.

Marks	$15-20$	$20-25$	$25-30$	$30-35$	$35-40$	$40-45$	$45-50$	Total
No. of students	$7$	$9$	$15$	$11$	$5$	$2$	$1$	$50$

$(ii)$ 'Less than' type cumulative frequency distribution :

Less than marks	$15$	$20$	$25$	$30$	$35$	$40$	$45$	$50$
Cumulative frequency	$0$	$7$	$16$	$31$	$42$	$47$	$49$	$50$

'More than' type cumulative frequency distribution:

More than marks	$15$	$20$	$25$	$30$	$35$	$40$	$45$	$50$
Cumulative frequency	$50$	$43$	$34$	$19$	$8$	$3$	$1$	$0$

$(iii)$ $7$ $(iv)$ $19$

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