Tag: maths

Questions Related to maths

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.

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

  1. $a$

  2. $b$

  3. $c$

  4. $d$

Show answer
Correct Option: B,D
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.

An ogive curve is 

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

  1. Histogram

  2. Frequency polygon

  3. Cumulative frequency

  4. All the above

Show answer
Correct Option: A

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 $200$ $240$ $300$ $50$
maths interpreting data and graphs histograms for non-uniform class widths histograms with unequal class intervals revisiting histograms

  1. Rs. $8000$

  2. Rs. $8350$

  3. Rs. $8500$

  4. Rs. $8750$

Show answer
Correct Option: B
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 = $8350$

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

  1. 21.2 Rs.

  2. 22.2 Rs.

  3. 23.2 Rs.

  4. 24.2 Rs.

Show answer
Correct Option: C
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 = $23.2$

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 $=Women$

Convert the following percents into fractions:

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

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

  1. $\dfrac{99}{100}$

  2. $\dfrac{3}{100}$

  3. $\dfrac{33}{100}$

  4. $\dfrac{1}{3}$

Show answer
Correct Option: D
Explanation:

Given percent  $={33}\dfrac{1}{3}\%$

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

Convert the following percents into fractions:

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

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

  1. $\dfrac{2}{16}$

  2. $\dfrac{1}{16}$

  3. $\dfrac{25}{4}$

  4. $\dfrac{1}{4}$

Show answer
Correct Option: B
Explanation:
Given percent $={6}\dfrac{1}{4}\%$
Now, ${6}\dfrac{1}{4}=\dfrac{(6\times4)+1}{4}$
                 $=\dfrac{25}{4}$
$\implies{6}\dfrac{1}{4}\%=\dfrac {25}{4}\times\dfrac{1}{100}$
                      $=\dfrac {1} {16}$