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Questions Related to maths

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

For which of these would you use a histogram to show the data?
$(a)$ The number of letters for different areas in a postman's bag.
$(b)$ The height of competitors in an athletics meet.
$(c)$ The number of cassettes produced by $5$ companies.
$(d)$ The number of passengers boarding trains from $7{:}00$ a.m. to $7{:}00$ p.m. at a station.
Give reasons for each.

  1. $a$
  2. $b$
  3. $c$
  4. $d$
Reveal answer Fill a bubble to check yourself
B,D Correct answer
Explanation

Histograms are a special form of bar chart where the data represents continuously rather than discrete categories. This means that in a histogram there are no gaps between the columns representing the different categories.

The height of competitors are continuous data. There are no gaps between the data. 
Even the train timings are continuous data.   
Hence, option B and C are correct.

Multiple choice maths interpreting data and graphs histograms for non-uniform class widths histograms with unequal class intervals revisiting histograms

Draw the histogram and use it to find the mode for the following frequency distribution.

House - Rent in Rs. per month $4000 - 6000$ $6000 - 8000$ $8000 - 10000$ $10000 - 12000$
Number of families $200$ $240$ $300$ $50$
  1. Rs. $8000$
  2. Rs. $8350$
  3. Rs. $8500$
  4. Rs. $8750$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
max. frequency = $300$
so group is = $8000-10000$
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 = $8000+ \dfrac{300-240}{2\times 300-240-50}\times 2000$
mode= $8000+387.096$
mode = $8387.096$
mode = $8350$
Multiple choice maths interpreting data and graphs histograms for non-uniform class widths histograms with unequal class intervals revisiting histograms

Represent the following data by histogram and hence compute mode.

Price of sugar per kg (in Rs.) 18 - 20 20 - 22 22 - 24 24 - 26 26 - 28 Total
Number of weeks 4 8 22 12 6 52

  1. 21.2 Rs.

  2. 22.2 Rs.

  3. 23.2 Rs.

  4. 24.2 Rs.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
max. frequency = $22$
so group is = $22-24$
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 = $22+ \dfrac{22-8}{2\times 22-8-12}\times 2$
mode= $22+1.167$
mode = $23.167$
mode = $23.2$
Multiple choice maths graphical representation histograms for non-uniform class widths histograms with unequal class intervals revisiting histograms

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
  1. $146\ cm$
  2. $147\ cm$
  3. $149\ cm$
  4. $150\ cm$
Reveal answer Fill a bubble to check yourself
B Correct answer
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 = $147$
Multiple choice maths graphical representation histograms for non-uniform class widths histograms with unequal class intervals revisiting histograms

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

  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.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Histograms are used to represent continuous frequency distributions, such as the heights of competitors grouped into continuous class intervals. The other options represent discrete categories or counts where bar graphs are more appropriate.

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

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: 

  1. Women

  2. Men

  3. Boy

  4. Girl
Reveal answer Fill a bubble to check yourself
A Correct answer
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 $=Women$

Multiple choice maths percent use of percentages converting between fractions or decimals and percentages percentage of a quantity

Convert the following percents into fractions:

$33\dfrac{1}{3}\%$

  1. $\dfrac{99}{100}$
  2. $\dfrac{3}{100}$
  3. $\dfrac{33}{100}$
  4. $\dfrac{1}{3}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given percent  $={33}\dfrac{1}{3}\%$

Now, ${33}\dfrac{1}{3}=\dfrac{(33\times3)+1}{3}=\dfrac{100}{3}$
${33}\dfrac{1}{3}\%=\dfrac {100}{3}\times\dfrac{1}{100}=\dfrac {1} {3}$

Multiple choice maths percent use of percentages converting between fractions or decimals and percentages percentage of a quantity

Convert the following percents into fractions:

$6\dfrac{1}{4}\%$

  1. $\dfrac{2}{16}$
  2. $\dfrac{1}{16}$
  3. $\dfrac{25}{4}$
  4. $\dfrac{1}{4}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Given percent $={6}\dfrac{1}{4}\%$
Now, ${6}\dfrac{1}{4}=\dfrac{(6\times4)+1}{4}$
                 $=\dfrac{25}{4}$
$\implies{6}\dfrac{1}{4}\%=\dfrac {25}{4}\times\dfrac{1}{100}$
                      $=\dfrac {1} {16}$