Tag: histograms with unequal class intervals

Questions Related to histograms with unequal class intervals

The diagram used to estimate mode of continuous frequency distribution graphically is _____

maths bar graphs histograms for non-uniform class widths histograms with unequal class intervals revisiting histograms

  1. histogram

  2. frequency curve

  3. bar diagram

  4. all of these

Show answer
Correct Option: A
Explanation:

It is fundamental concept that histogram is used to obtain mode from continuous frequency distribution graphically.

Represent the following data using histogram, hence find the mode.

Height of students (cm) 140 - 144 145 - 149 150 - 154 155 - 159
Number of students 2 12 10 4
maths graphical representation histograms for non-uniform class widths histograms with unequal class intervals revisiting histograms

  1. $146\  cm$

  2. $147\  cm$

  3. $149\  cm$

  4. $150\  cm$

Show answer
Correct Option: B
Explanation:
max. frequency = $12$
so group is = $145-149$
so mode = $L+\dfrac{f _{1}-f _{0}}{2f _{1}-f _{0}-f _{2}}\times w$
$L$= lower class boundary of the modal group
$f _{1}$ = frequency of the modal group
$f _{0}$= frequency of the class preceding or just before the modal class
$f _{2}$ = frequency of the class succeeding or just after the modal class
$w$= group width
mode = $145+ \dfrac{12-2}{2\times 12-2-10}\times 4$
mode= $145+3.333$
mode = $148.333$
mode = $147$

For which of these would you use a histogram to show the data?

maths graphical representation histograms for non-uniform class widths histograms with unequal class intervals revisiting histograms

  1. The number of letters for different areas in a postman's bag.

  2. The height of competitors in an athletics meet

  3. The number of cassettes produced by 5 companies

  4. The number of passengers boarding trains from 7:00 a.m. to 7:00 p.m. from a station.

Show answer
Correct Option: A

The shoppers who come to a departmental store are marked as : man (M), woman (W), boy (B) or girl (G). The following list gives the shoppers who came during the first hour in the morning.
W W W G B W W M G G M M W W W
W G B M W B G G M W W M M W W
W M W B W G M W W W W G W M M
W W M W G W M G W M M B G  G W

The mode shoppers are: 

maths graphical representation histograms for non-uniform class widths histograms with unequal class intervals revisiting histograms

  1. Women

  2. Men

  3. Boy

  4. Girl

Show answer
Correct Option: A
Explanation:

From the question we are going to form frequency table :

$Shoppers$  $No.\,of\,shoppers$ 
$M$  $15$ 
$W$  $28$ 
$B$  $5$ 
$G$  $12$ 

From table we can see, $Women(W)$ has maximum number of shoppers.

$\therefore$  The mode shoppers are $=Women$