Mathematics>Statistics and Probability>Statistics>Mode of Grouped Data

Mode of Grouped Data

IMPORTANT

Mode of Grouped Data: Overview

This topic covers concepts, such as, Mode, Modal Class in Grouped Data & Mode of Grouped Data etc.

Important Questions on Mode of Grouped Data

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IMPORTANT

Mathematics>Statistics>Mode of Grouped Data> Q 1

If mode of the following frequency distribution is $55$ , then find the value of $x$ .

Class:	0-15	15-30	30-45	45-60	60-75	75-90
Frequency:	10	7	x	15	10	12

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Mathematics>Statistics>Mode of Grouped Data> Q 2

The marks distribution of $30$ students in a science examination are as follows. Find the mode of this data.

Marks obtained $(x_{i})$	$10$	$20$	$36$	$40$	$50$	$56$	$60$	$70$	$72$	$80$	$88$	$92$	$95$
Number of students $(f_{i})$	$1$	$1$	$3$	$4$	$3$	$2$	$4$	$4$	$1$	$1$	$2$	$3$	$1$

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Mathematics>Statistics>Mode of Grouped Data> Q 3

Find the mode of the following distribution:

Height (in cm)	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$	$80 - 90$
No. of plants	$4$	$3$	$8$	$12$	$6$	$2$

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Mathematics>Statistics>Mode of Grouped Data> Q 4

Find the mode from the following information: $L = 10, h = 2, f_{0} = 58, f_{1} = 70, f_{2} = 42$ .

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Mathematics>Statistics>Mode of Grouped Data> Q 5

Find the mode of the following frequency distribution (correct to two decimal places):-

Class	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
$f_{i}$	$6$	$10$	$13$	$7$	$4$

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Mathematics>Statistics>Mode of Grouped Data> Q 6

The mode from following frequency distribution is:

Class	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$	$30 - 35$	$35 - 40$	$40 - 45$
Frequency	$3$	$7$	$16$	$12$	$9$	$5$	$3$

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Mathematics>Statistics>Mode of Grouped Data> Q 7

Find the mode from following frequency distribution:

Height (in $cm$ )	$52 - 55$	$55 - 58$	$58 - 61$	$61 - 64$
Number of students	$10$	$20$	$25$	$10$

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Mathematics>Statistics>Mode of Grouped Data> Q 8

On sports day of a school, age-wise participation of students is shown in the following distribution.

Age (in years)	$5 - 7$	$7 - 9$	$9 - 11$	$11 - 13$	$13 - 15$	$15 - 17$	$17 - 19$
Number of students	$x$	$15$	$18$	$30$	$50$	$48$	$x$

Find the mode of the data. Also, find missing frequencies when the sum of frequencies is $181$ .

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Mathematics>Statistics>Mode of Grouped Data> Q 9

Given below is the frequency distribution of the heights of players in a school

Height (in cm)	Number of students
$160 - 163$	$18$
$164 - 167$	$116$
$168 - 171$	$142$
$172 - 175$	$129$
$176 - 179$	$80$
$180 - 183$	$15$

Determine the modal height.

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Mathematics>Statistics>Mode of Grouped Data> Q 10

Find the mode of the following data:-

Class interval	$0 - 9$	$10 - 19$	$20 - 29$	$30 - 39$	$40 - 49$	$50 - 59$
Frequency	$12$	$15$	$21$	$17$	$19$	$6$

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Mathematics>Statistics>Mode of Grouped Data> Q 11

Some surnames were picked up from a local telephone directory and the frequency distribution of the number of letters of the English alphabets was obtained as follows:-

Number of letters	$1 - 4$	$4 - 7$	$7 - 10$	$10 - 13$	$13 - 16$	$16 - 19$
Number of surnames	$10$	$25$	$35$	$x$	$12$	$8$

If it is given that mode of the distribution is $8$ , then find the missing frequency $(x)$ .

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Mathematics>Statistics>Mode of Grouped Data> Q 12

The monthly consumption of electricity of some consumers is given below as a distribution.

Monthly consumption (in units)	Number of consumers
$90 - 120$	$20$
$120 - 150$	$15$
$150 - 180$	$x$
$180 - 210$	$75$
$210 - 240$	$50$

Find the missing frequency $(x)$ , if the mode of distribution is given to be $200$ units.

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Mathematics>Statistics>Mode of Grouped Data> Q 13

The mode of the following data is $36$ . Find the missing frequency $x$ in it.

Class	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$
Frequency	$8$	$10$	$x$	$16$	$12$	$6$	$7$

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Mathematics>Statistics>Mode of Grouped Data> Q 14

The weight of coffee in $70$ packets are shown in the following table.

Weight (in grams)	Number of packets
$200 - 201$	$12$
$201 - 202$	$26$
$202 - 203$	$20$
$203 - 204$	$9$
$204 - 205$	$2$
$205 - 206$	$1$

Determine the modal weight.

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Mathematics>Statistics>Mode of Grouped Data> Q 15

The following table shows the age distribution of cases of a certain disease admitted during a year in a particular hospital

Age (in years)	Number of cases
$0 - 10$	$5$
$10 - 20$	$8$
$20 - 30$	$7$
$30 - 40$	$12$
$40 - 50$	$28$
$50 - 60$	$20$
$60 - 70$	$10$
$70 - 80$	$10$

Find the average age for which maximum case occurred.

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Mathematics>Statistics>Mode of Grouped Data> Q 16

For the following data, find the mode.

Class	$1 - 3$	$3 - 5$	$5 - 7$	$7 - 9$	$9 - 11$
Frequency	$14$	$16$	$4$	$4$	$2$

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Mathematics>Statistics>Mode of Grouped Data> Q 17

Find the mode of the given data.

Marks	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$
Frequency	$15$	$6$	$18$	$10$

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Mathematics>Statistics>Mode of Grouped Data> Q 18

Find the mode of the following distributions:

Class	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$
Frequency	$3$	$15$	$24$	$8$	$5$

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Mathematics>Statistics>Mode of Grouped Data> Q 19

Find the mode of the following distributions:

Class	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
Frequency	$4$	$7$	$13$	$9$	$3$

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Mathematics>Statistics>Mode of Grouped Data> Q 20

Mode value of any series is :