Find the mode of the following distribution by drawing a histogram Mid value 12 18 24 30 36 42 48 Frequency 20 12 8 24 16 8 12 Also state the modal class.

Mid value Frequency Class interval 12 20 9 - 15 18 12 15 - 21 24 8 21 - 27 30 24 27 - 33 36 16 33 - 39 42 8 39 - 45 48 12 45 - 51 It is easy to see that the highest frequency is 24 corresponding to this class interval is 27 - 33 . Hence, The modal class is 27 - 33 . We construct the relevant portion of histogram and estimate mode from it: Since mode is dependent only on neighbourhood frequencies, drawing the rectangle corresponding to modal class and adjoining two classes. Joining the ends of opposite rectangles by straight lines - the point of intersection corresponds to mode. The two lines meet at a point A , which corresponds to x - value of 31 . Hence, Mode = 31 .

The following data gives distribution of heights of a group of 60 college students: Height(in cms) Number of students 145 - 149 . 9 2 150 - 154 . 9 5 155 - 159 . 9 9 160 - 164 . 9 15 165 - 169 . 9 16 170 - 174 . 9 7 175 - 179 . 9 5 180 - 184 . 9 1 Draw the histogram for this distribution and find the modal height. Check this result by using algebraic formula.

Histogram representing given data is: Modal height is represented by point P ( 165 . 5 , 15 . 1 ) ⇒ Modal Height = 165 . 5 c m Finding Modal Height by Algebraic method(Converting discontinuous grouped data to continuous grouped data): Height (in cms) f 144 . 95 - 149 . 95 2 149 . 95 - 154 . 95 5 154 . 95 - 159 . 95 9 159 . 95 - 164 . 95 15 164 . 95 - 169 . 95 16 169 . 95 - 174 . 95 7 174 . 95 - 179 . 95 5 179 . 95 - 184 . 95 1 As the trend of frequencies is regular increase-decrease pattern, The Modal class is the class with the highest frequency i.e, 164 . 95 - 169 . 95 Mode is given by the formula Mode = l + f 1 - f 0 2 f 1 - f 0 - f 2 × C l = 164 . 95 , f 1 = 16 , f 0 = 15 , f 2 = 7 , C = 5 Mode = 164 . 95 + 16 - 15 2 × 16 - 15 - 7 × 5 = 165 . 45 Therefore, Modal Height = 165 . 45 cm

Pocket money (in ₹ , per month) of 30 students is 75 70 71 55 38 52 40 48 60 65 35 58 70 61 65 64 63 58 50 53 62 64 66 65 75 64 57 60 63 45 Form a frequency table with a grouping of 30 - 40 , 40 - 50 etc. Also find the modal pocket money (by graphical method) as well as by using formula.

Pocket Money Number of students f 30 - 40 3 40 - 50 3 50 - 60 8 60 - 70 13 70 - 80 3 Σ f = 30 Since, 13 is the highest frequency, corresponds to this modal class is 60 - 70 . As we know, Mode = l + f m - f m - 1 2 f m - f m - 1 - f m + 1 × h Here, lower limit of the modal class = l = 60 , Frequency of the modal class = f m = 13 , Frequency of the class preceding the modal class = f m - 1 = 8 , Frequency of the class succeeding the modal class = f m + 1 = 3 Width of the modal class = h = 10 , Mode = 60 + ( 13 - 8 ) ( 2 × 13 - 8 - 3 ) × 10 = 60 + 5 15 × 10 = 60 + 3 · 33 Mode = 63 . 33 By graphically, We construct a relevant portion of the histogram and estimate it:- Since mode is dependent only on neighbourhood frequencies, drawing the rectangle corresponding to modal class and adjoining two classes. Joining the ends of opposite rectangles by straight lines. The point of intersection of these straight lines corresponds to mode. Two lines meet at point A , which corresponds to value of 63 . 3 ₹ Hence, by graphically, mode = 63 . 3 ₹ By formula, mode = 63 . 33 ₹

Draw a histogram for the following distribution: Wt. in kg 40 - 44 45 - 49 50 - 54 55 - 59 60 - 64 65 - 69 Number of students 2 8 12 10 6 4 Hence, estimate the modal weight.

Wt in kg Number of students ( f ) 40 - 44 2 45 - 49 8 50 - 54 12 55 - 59 10 60 - 64 6 65 - 69 4 It is easy to see that the highest frequency is 12 corresponding to this class interval is 50 - 54 . The modal class is 50 - 54 Now constructing a histogram of given data: Since mode is dependent only on neighbourhood frequencies, drawing the rectangle corresponding to modal class and adjoining two classes. Joining the ends of opposite rectangles by straight lines - the point of intersection corresponds to mode. The Two lines meet at point A , which corresponds to value of 53 . Mode = 53 kg .

MEDIUM

Earn 100

How is the mode calculated by the graphical method? Explain.

Important Questions on Statistics

EASY

Mathematics>Statistics>Statistics>Finding Mode

Find the mode from the following data:

Class :	$3 - 6$	$6 - 9$	$9 - 12$	$12 - 15$	$15 - 18$	$18 - 21$	$21 - 24$
Frequency	$2$	$5$	$10$	$23$	$21$	$12$	$3$

EASY

Mathematics>Statistics>Statistics>Finding Mode

For a distribution Mean, Median and Mode are

23, 24

and

25.5

respectively, then it is most likely__________ skewed distribution

EASY

Mathematics>Statistics>Statistics>Finding Mode

Find the mode of the following distribution.

Class :	$0 - 7$	$7 - 14$	$14 - 21$	$21 - 28$	$28 - 35$	$35 - 42$	$42 - 49$
Frequency	$19$	$25$	$36$	$72$	$51$	$43$	$28$

EASY

Mathematics>Statistics>Statistics>Finding Mode

Determine the value of the mode for the following sets of data:

$10, 11, 10, 12, 11, 10, 11, 11, 11, 12, 13, 11, 12$

HARD

Mathematics>Statistics>Statistics>Finding Mode

Find the mode of the following distribution by drawing a histogram

Mid value	$12$	$18$	$24$	$30$	$36$	$42$	$48$
Frequency	$20$	$12$	$8$	$24$	$16$	$8$	$12$

Also state the modal class.

EASY

Mathematics>Statistics>Statistics>Finding Mode

The mode of the data

8, 11, 9, 8, 11, 9, 7, 8, 7, 3, 2

is ______.

EASY

Mathematics>Statistics>Statistics>Finding Mode

Find the mode of this set of data :

$34, 31, 37, 44, 34, 37, 34, 44, 31, 31, 34, 44, 43, 34, 31, 42, 44, 34, 42, 43, 34, 44, 31, 43, 42$

EASY

Mathematics>Statistics>Statistics>Finding Mode

What is the mode for the data

20, 20, 20, 21, 21, 21, 21, 21, 22, 22, 22, 22, 22, 22, 22, 23, 23, 23, 23, 23, 24, 24

and

25

EASY

Mathematics>Statistics>Statistics>Finding Mode

The mode of the series

3, 4, 2, 6, 1, 7, 6, 7, 6, 8, 9, 5

HARD

Mathematics>Statistics>Statistics>Finding Mode

The histogram below represents the scores obtained by $25$ students in a Mathematics mental test. Use the data to:

To determine the modal class.

Question Image

HARD

Mathematics>Statistics>Statistics>Finding Mode

The following data gives distribution of heights of a group of 60 college students:

Height(in cms)	Number of students
$145 - 149.9$	$2$
$150 - 154.9$	$5$
$155 - 159.9$	$9$
$160 - 164.9$	$15$
$165 - 169.9$	$16$
$170 - 174.9$	$7$
$175 - 179.9$	$5$
$180 - 184.9$	$1$

Draw the histogram for this distribution and find the modal height. Check this result by using algebraic formula.

HARD

Mathematics>Statistics>Statistics>Finding Mode

Pocket money (in $₹$ , per month) of $30$ students is

$75$	$70$	$71$	$55$	$38$	$52$	$40$	$48$	$60$	$65$
$35$	$58$	$70$	$61$	$65$	$64$	$63$	$58$	$50$	$53$
$62$	$64$	$66$	$65$	$75$	$64$	$57$	$60$	$63$	$45$

Form a frequency table with a grouping of $30 - 40, 40 - 50$ etc. Also find the modal pocket money (by graphical method) as well as by using formula.

EASY

Mathematics>Statistics>Statistics>Finding Mode

The mode of a set of observations $7, 12, 8, 5, 6, 4, 9, 10, 8, 9, 7, 9, 6, 5, 9$ is,

MEDIUM

Mathematics>Statistics>Statistics>Finding Mode

Draw a histogram for the following distribution:

Wt. in $kg$	$40 - 44$	$45 - 49$	$50 - 54$	$55 - 59$	$60 - 64$	$65 - 69$
Number of students	$2$	$8$	$12$	$10$	$6$	$4$

Hence, estimate the modal weight.

EASY

Mathematics>Statistics>Statistics>Finding Mode

The mode of the data

8, 11, 9, 8, 11, 9, 7, 8, 7, 3, 2

EASY

Mathematics>Statistics>Statistics>Finding Mode

The mode of the distribution for the following data is:

$4, 5, 6, 7, 8, 6, 5, 6, 10, 8, 3$

EASY

Mathematics>Statistics>Statistics>Finding Mode

Determine the value of the mode for the following sets of data:

$x$	$14$	$15$	$16$	$17$	$18$	$19$	$20$
$f$	$14$	$26$	$18$	$9$	$2$	$1$	$1$

EASY

Mathematics>Statistics>Statistics>Finding Mode

In a class test, the marks (out of $10$ ) of $30$ students were:

$5, 3, 6, 5, 5, 4, 1, 3, 8, 4, 3, 6, 5, 4, 8, 2, 5, 4, 4, 4, 3, 7, 2, 4, 5, 4, 8, 9, 10, 7$

Draw a tally chart and a frequency table. Hence, find

the mode

MEDIUM

Mathematics>Statistics>Statistics>Finding Mode

Read the three given statements carefully and then which of the following statements are correct?
(i) A histogram can be used to compute the mode
(ii) When there is change of scale, the median is affected
(iii) Variance is not affected when there is change of origin and scale

MEDIUM

Mathematics>Statistics>Statistics>Finding Mode

Consider the following statements

(i)

Mode can be computed from histogram

(ii)

Median is not independent of change of scale

(iii)

Variance is independent of change of origin and scale

Which of these is - are correct

How is the mode calculated by the graphical method? Explain.

Important Questions on Statistics

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