Frequency Distribution

IMPORTANT

Frequency Distribution: Overview

This Topic covers sub-topics such as Class Intervals, Cumulative Frequency Distribution, Continuous Frequency Distribution, Discrete Frequency Distribution, Bivariate Frequency Distribution and, Relative Cumulative Frequency Distribution

Important Questions on Frequency Distribution

HARD

IMPORTANT

mathematics>Classification and Tabulation of Data>Frequency Distribution> Q 1

The daily journey times for $80$ factory staff to get to work are given in the table.

Time $(t)$	$t < 10$	$t < 15$	$t < 20$	$t < 25$	$t < 30$	$t < 45$	$t < 60$
Number of staff $(c f)$	$3$	$11$	$24$	$56$	$68$	$76$	$80$

Find the exact number of staff who take $\frac{x + y}{2}$ minutes or more to get to work, given that $85 %$ of the staff take less than $x$ minutes and that $70 %$ of the staff take $y$ minutes or more.

HARD

IMPORTANT

mathematics>Classification and Tabulation of Data>Frequency Distribution> Q 2

Find the less than and more than cumulative frequencies for the following distribution

Classes	$15 - 20$	$20 - 25$	$25 - 30$	$30 - 35$	$35 - 40$	$40 - 45$	Total
Frequencies	$5$	$8$	$17$	$24$	$16$	$10$	$80$

Also find the relative cumulative frequencies respectively.

HARD

IMPORTANT

mathematics>Classification and Tabulation of Data>Frequency Distribution> Q 3

Construct frequency distribution table for the following data by Inclusive method

$67, 34, 36, 48, 49, 31, 61, 34, 43, 45, 38, 32, 27, 61, 29, 47, 36, 50, 46, 30, 46, 32, 30, 33, 45, 49, 48, 41, 53, 36, 37, 47, 47, 30, 46, 57, 39, 45, 42, 37$

Also, find the relative-cumulative frequency distribution.

MEDIUM

IMPORTANT

mathematics>Classification and Tabulation of Data>Frequency Distribution> Q 4

Construct a bivariate frequency distribution table of the marks obtained by students in Statistics $(X)$ and English $(Y)$ .

Marks in Statistics $(X)$	$37$	$20$	$46$	$28$	$35$	$26$	$41$	$48$	$32$	$23$	$20$	$39$	$47$	$33$	$27$	$26$
Marks in English $(Y)$	$30$	$32$	$41$	$33$	$29$	$43$	$30$	$21$	$44$	$38$	$47$	$24$	$32$	$21$	$20$	$21$

Construct a bivariate frequency distribution table for the given data by taking class intervals $20 - 30, 30 - 40, . . . . . .$ etc. for both $X$ and $Y$ .

MEDIUM

IMPORTANT

mathematics>Classification and Tabulation of Data>Frequency Distribution> Q 5

For the below frequency table:

Data value	Frequency
$2$	$3$
$3$	$5$
$4$	$3$
$5$	$6$
$6$	$2$
$7$	$1$

Find relative cumulative frequency for each data value.

MEDIUM

IMPORTANT

mathematics>Classification and Tabulation of Data>Frequency Distribution> Q 6

The table shows the amount, in inches, of annual rainfall in a sample of towns:

Rainfall (inches)	Frequency
$2.95 - 4.97$	$6$
$4.97 - 6.99$	$7$
$6.99 - 9.01$	$15$
$9.01 - 11.03$	$8$
$11.03 - 13.05$	$9$
$13.05 - 15.07$	$5$

Find relative cumulative frequency for each class.

EASY

IMPORTANT

mathematics>Classification and Tabulation of Data>Frequency Distribution> Q 7

The weights of $121$ sausages are summarised in the following table.

Weight (grams)	$< 25$	$< 35$	$< 45$	$< 50$	$< 60$	$< 65$	$< 80$
Cumulative frequency	$0$	$17$	$38$	$59$	$72$	$89$	$121$

State how many sausages weighed between $45 g$ and $50 g$ .

EASY

IMPORTANT

mathematics>Classification and Tabulation of Data>Frequency Distribution> Q 8

The weights of $230$ sausages are summarised in the following table.

Weight (grams)	$< 20$	$< 30$	$< 40$	$< 45$	$< 50$	$< 60$	$< 70$
Cumulative frequency	$0$	$10$	$60$	$120$	$150$	$210$	$230$

State how many sausages weighed between $20 g$ and $30 g$ .

EASY

IMPORTANT

mathematics>Classification and Tabulation of Data>Frequency Distribution> Q 9

The weights of $230$ sausages are summarised in the following table.

Weight (grams)	$< 20$	$< 30$	$< 40$	$< 45$	$< 50$	$< 60$	$< 70$
Cumulative frequency	$0$	$10$	$60$	$120$	$150$	$210$	$230$

State how many sausages weighed between $60 g$ and $70 g$ .

EASY

IMPORTANT

mathematics>Classification and Tabulation of Data>Frequency Distribution> Q 10

The weights of $230$ sausages are summarised in the following table.

Weight (grams)	$< 20$	$< 30$	$< 40$	$< 45$	$< 50$	$< 60$	$< 70$
Cumulative frequency	$0$	$20$	$50$	$100$	$160$	$210$	$230$

State how many sausages weighed between $60 g$ and $70 g$ .

EASY

IMPORTANT

mathematics>Classification and Tabulation of Data>Frequency Distribution> Q 11

The weights of $220$ sausages are summarised in the following table.

Weight (grams)	$< 20$	$< 30$	$< 40$	$< 45$	$< 50$	$< 60$	$< 70$
Cumulative frequency	$0$	$20$	$50$	$100$	$160$	$210$	$220$

State how many sausages weighed between $20 g$ and $30 g$ .

EASY

IMPORTANT

mathematics>Classification and Tabulation of Data>Frequency Distribution> Q 12

The weights of $220$ sausages are summarised in the following table.

Weight (grams)	$< 20$	$< 30$	$< 40$	$< 45$	$< 50$	$< 60$	$< 70$
Cumulative frequency	$0$	$20$	$50$	$100$	$160$	$210$	$220$

State how many sausages weighed between $60 g$ and $70 g$ .

EASY

IMPORTANT

mathematics>Classification and Tabulation of Data>Frequency Distribution> Q 13

The weights of $220$ sausages are summarised in the following table.

Weight (grams)	$< 20$	$< 30$	$< 40$	$< 45$	$< 50$	$< 60$	$< 70$
Cumulative frequency	$0$	$20$	$50$	$100$	$160$	$210$	$220$

State how many sausages weighed between $50 g$ and $60 g$ .

EASY

IMPORTANT

mathematics>Classification and Tabulation of Data>Frequency Distribution> Q 14

The densities, $d g / {cm}^{3}$ , of $107$ chemical compounds are given in the following table.

\begin{array}{l} Density (dg / {cm}^{3}) & d < 1.20 & d < 1.30 & d < 1.40 & d < 1.58 & d < 1.80 \\ Number of compounds (c f) & 17 & 25 & 49 & 81 & 107 \end{array}

Find the frequencies $a, b, c$ and $d$

Density $(d g / {cm}^{3})$	$0 -$	$1.20 -$	$1.30 -$	$1.40 - 1.80$
Number of compounds $(f)$	$a$	$b$	$c$	$d$

EASY

IMPORTANT

mathematics>Classification and Tabulation of Data>Frequency Distribution> Q 15

The densities, $d g / {cm}^{3}$ , of $107$ chemical compounds are given in the following table.

\begin{array}{l} Density (dg / {cm}^{3}) & d < 1.20 & d < 1.30 & d < 1.40 & d < 1.58 & d < 1.80 \\ No. compounds (c f) & 33 & 44 & 76 & 97 & 107 \end{array}

Find the frequencies $a, b, c$ and $d$

Density $(d g / {cm}^{3})$	$0 -$	$1.20 -$	$1.30 -$	$1.40 - 1.80$
No. compounds $(f)$	$a$	$b$	$c$	$d$

EASY

IMPORTANT

mathematics>Classification and Tabulation of Data>Frequency Distribution> Q 16

The densities, $d g / {cm}^{3}$ , of $105$ chemical compounds are given in the following table.

\begin{array}{l} Density (dg / {cm}^{3}) & d < 1.30 & d < 1.38 & d < 1.42 & d < 1.58 & d < 1.70 \\ No. compounds (c f) & 33 & 44 & 76 & 97 & 105 \end{array}

Find the frequencies $a, b, c$ and $d$

Density $(d g / {cm}^{3})$	$0 -$	$1.30 -$	$1.38 -$	$1.42 - 1.70$
No. compounds $(f)$	$a$	$b$	$c$	$d$

EASY

IMPORTANT

mathematics>Classification and Tabulation of Data>Frequency Distribution> Q 17

The densities, $d g / {cm}^{3}$ , of $129$ chemical compounds are given in the following table.

Density $(d g / {cm}^{3})$	$d < 1.30$	$d < 1.38$	$d < 1.42$	$d < 1.58$	$d < 1.70$
No. compounds $(c f)$	$42$	$61$	$88$	$100$	$121$

Find the frequencies $a, b, c$ and $d$ given in the table below.

Density $(d g / {cm}^{3})$	$0 -$	$1.30 -$	$1.38 -$	$1.42 - 1.70$
No. compounds $(f)$	$a$	$b$	$c$	$d$

EASY

IMPORTANT

mathematics>Classification and Tabulation of Data>Frequency Distribution> Q 18

The densities, $d g / {cm}^{3}$ , of $129$ chemical compounds are given in the following table.

Density $(d g / {cm}^{3})$	$d < 1.30$	$d < 1.38$	$d < 1.42$	$d < 1.58$	$d < 1.70$
No. compounds $(c f)$	$32$	$57$	$92$	$117$	$135$

Find the frequencies $a, b, c$ and $d$ given in the table below.

Density $(d g / {cm}^{3})$	$0 -$	$1.30 -$	$1.38 -$	$1.42 - 1.70$
No. compounds $(f)$	$a$	$b$	$c$	$d$

EASY

IMPORTANT

mathematics>Classification and Tabulation of Data>Frequency Distribution> Q 19

The densities, $d g / {cm}^{3}$ , of $129$ chemical compounds are given in the following table.

Density $(d g / {cm}^{3})$	$d < 1.30$	$d < 1.38$	$d < 1.42$	$d < 1.58$	$d < 1.70$
No. compounds $(c f)$	$32$	$77$	$92$	$107$	$129$

Find the frequencies $a, b, c$ and $d$ given in the table below.

Density $(d g / {cm}^{3})$	$0 -$	$1.30 -$	$1.38 -$	$1.42 - 1.70$
No. compounds $(f)$	$a$	$b$	$c$	$d$

EASY

IMPORTANT

mathematics>Classification and Tabulation of Data>Frequency Distribution> Q 20

Construct frequency distribution table for the following data by Inclusive method

$22, 21, 37, 39, 37, 41, 43, 23, 27, 35, 33, 30, 29, 27, 47, 40, 31, 32, 41, 45, 34, 49, 23, 24, 27, 36, 44, 42, 39, 38, 28, 33, 42, 33, 46, 23, 34, 41, 40, 30, 45, 42, 38, 37, 38, 42, 44, 47, 28, 37$

Frequency Distribution

Frequency Distribution: Overview

Important Questions on Frequency Distribution

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