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Presentation of data — Statistics STD 11 Commerce — Question

Gujarat BoardEnglish MediumSTD 11 CommerceStatisticsPresentation of data5 Marks
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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