(A) To find the mean marks,we calculate the product of each mark $(x_{i})$ with its corresponding frequency $(f_{i})$.Marks obtained $(x_{i})$Number o

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(A) To find the mean marks,we calculate the product of each mark $(x_{i})$ with its corresponding frequency $(f_{i})$.Marks obtained $(x_{i})$Number of students $(f_{i})$$f_{i}x_{i}$$10$$1$$10$$20$$1$$20$$36$$3$$108$$40$$4$$160$$50$$3$$150$$56$$2$$112$$60$$4$$240$$70$$4$$280$$72$$1$$72$$80$$1$$80$$88$$2$$176$$92$$3$$276$$95$$1$$95$Total$\Sigma f_{i} = 30$$\Sigma f_{i}x_{i} = 1779$The mean $\bar{x}$ is given by the formula:$\bar{x} = \frac{\Sigma f_{i}x_{i}}{\Sigma f_{i}} = \frac{1779}{30} = 59.3$Therefore,the mean marks obtained by the students is $59.3$.

Class 10 Mathematics Statistics Textbook - Statistics

Easy

The marks obtained by $30$ students of Class $X$ of a certain school in a Mathematics paper consisting of $100$ marks are presented in the table below. Find the mean of the marks obtained by the students.
Marks obtained $(x_{i})$ $10, 20, 36, 40, 50, 56, 60, 70, 72, 80, 88, 92, 95$
Number of students $(f_{i})$ $1, 1, 3, 4, 3, 2, 4, 4, 1, 1, 2, 3, 1$

A
$59.3$
B
$63.2$
C
$54.5$
D
$55.5$

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Class 10 Questions

Class 10

Mathematics Questions

Chapter

Statistics

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Textbook - Statistics

The following table shows the ages of the patients admitted in a hospital during a year:
Age (in years) $5$-$15$ $15$-$25$ $25$-$35$ $35$-$45$ $45$-$55$ $55$-$65$
Number of patients $6$ $11$ $21$ $23$ $14$ $5$

Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.

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The following table gives the production yield per hectare of wheat of $100$ farms of a village.
Production yield (in kg/ha) Number of farms
$50-55$ $2$
$55-60$ $8$
$60-65$ $12$
$65-70$ $24$
$70-75$ $38$
$75-80$ $16$

Change the distribution to a 'more than type' distribution,and draw its ogive.

Production yield (in kg/ha)	Number of farms
$50-55$	$2$
$55-60$	$8$
$60-65$	$12$
$65-70$	$24$
$70-75$	$38$
$75-80$	$16$

Medium

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$A$ life insurance agent found the following data for the distribution of ages of $100$ policy holders. Calculate the median age,if policies are given only to persons having age $18$ years onwards but less than $60$ years.
Age (in years) Number of policy holders
Below $20$ $2$
Below $25$ $6$
Below $30$ $24$
Below $35$ $45$
Below $40$ $78$
Below $45$ $89$
Below $50$ $92$
Below $55$ $98$
Below $60$ $100$

Difficult

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$100$ surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as follows:
Number of letters $1-4$ $4-7$ $7-10$ $10-13$ $13-16$ $16-19$
Number of surnames $6$ $30$ $40$ $16$ $4$ $4$

Determine the median number of letters in the surnames. Find the mean number of letters in the surnames. Also,find the modal size of the surnames.

Difficult

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Thirty women were examined in a hospital by a doctor and the number of heartbeats per minute were recorded and summarized as follows. Find the mean heartbeats per minute for these women,choosing a suitable method.
Number of heartbeats per minute $65$-$68$ $68$-$71$ $71$-$74$ $74$-$77$ $77$-$80$ $80$-$83$ $83$-$86$
Number of women $2$ $4$ $3$ $8$ $7$ $4$ $2$

Difficult

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Marks obtained $(x_{i})$	$10, 20, 36, 40, 50, 56, 60, 70, 72, 80, 88, 92, 95$
Number of students $(f_{i})$	$1, 1, 3, 4, 3, 2, 4, 4, 1, 1, 2, 3, 1$

Age (in years)	$5$-$15$	$15$-$25$	$25$-$35$	$35$-$45$	$45$-$55$	$55$-$65$
Number of patients	$6$	$11$	$21$	$23$	$14$	$5$

Age (in years)	Number of policy holders
Below $20$	$2$
Below $25$	$6$
Below $30$	$24$
Below $35$	$45$
Below $40$	$78$
Below $45$	$89$
Below $50$	$92$
Below $55$	$98$
Below $60$	$100$

Number of letters	$1-4$	$4-7$	$7-10$	$10-13$	$13-16$	$16-19$
Number of surnames	$6$	$30$	$40$	$16$	$4$	$4$

Number of heartbeats per minute	$65$-$68$	$68$-$71$	$71$-$74$	$74$-$77$	$77$-$80$	$80$-$83$	$83$-$86$
Number of women	$2$	$4$	$3$	$8$	$7$	$4$	$2$

Similar Questions

The following table gives the production yield per hectare of wheat of $100$ farms of a village.Production yield (in kg/ha)Number of farms$50-55$$2$$55-60$$8$$60-65$$12$$65-70$$24$$70-75$$38$$75-80$$16$Change the distribution to a 'more than type' distribution,and draw its ogive.

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The following table gives the production yield per hectare of wheat of $100$ farms of a village.
Production yield (in kg/ha) Number of farms
$50-55$ $2$
$55-60$ $8$
$60-65$ $12$
$65-70$ $24$
$70-75$ $38$
$75-80$ $16$

Change the distribution to a 'more than type' distribution,and draw its ogive.