Measures of Central Tendency

IMPORTANT

Measures of Central Tendency: Overview

This topic covers concepts, such as, Mean for Ungrouped Frequency Distribution: Discrete Frequency Distribution, Mean (Average) of Data, Relations between Mean & Median and Mode etc.

Important Questions on Measures of Central Tendency

HARD

IMPORTANT

Mathematics>Statistics>Measures of Central Tendency> Q 1

What are the merits and demerits of mode.

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

Age (in years)	$5 - 14$	$15 - 24$	$25 - 34$	$35 - 44$	$45 - 54$	$55 - 64$
Number of cases	$6$	$11$	$21$	$23$	$14$	$5$

Find the average age for which maximum cases occurred.

HARD

IMPORTANT

Mathematics>Statistics>Measures of Central Tendency> Q 2

What are the merits and demerits of mode.

Also find the average expenditure which is being done by the maximum number of manual workers for the following data that gives the distribution of total household expenditure (in $₹$ ) of manual workers in a city.

Expenditure (in $₹$ )	Frequency	Expenditure (in $₹$ )	Frequency
$1000 - 1500$	$24$	$3000 - 3500$	$30$
$1500 - 2000$	$40$	$3500 - 4000$	$22$
$2000 - 2500$	$33$	$4000 - 4500$	$16$
$2500 - 3000$	$28$	$4500 - 5000$	$7$

HARD

IMPORTANT

Mathematics>Statistics>Measures of Central Tendency> Q 3

What are the merits and demerits of mode.

Also compute the mode for the following grouped frequency distribution.

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

HARD

IMPORTANT

Mathematics>Statistics>Measures of Central Tendency> Q 4

What are the merits and demerits of mode.

Also compute the mode for the following frequency distribution.

Size of items	$0 - 4$	$4 - 8$	$8 - 12$	$12 - 16$	$16 - 20$	$20 - 24$	$24 - 28$	$28 - 32$	$32 - 36$	$36 - 40$
Frequency	$5$	$7$	$9$	$17$	$12$	$10$	$6$	$3$	$1$	$0$

HARD

IMPORTANT

Mathematics>Statistics>Measures of Central Tendency> Q 5

What are the properties of Mode.

Weight (in $g .$ )of $40$ eggs were recorded as given below:

Weight in $grams$	$85 - 89$	$90 - 94$	$95 - 99$	$100 - 104$	$105 - 109$
Number of eggs	$4$	$12$	$14$	$8$	$2$

Find the modal weight.

MEDIUM

IMPORTANT

Mathematics>Statistics>Measures of Central Tendency> Q 6

What are the properties of Mode.

A survey conducted on $20$ households in a locality by a group of students resulted in the following frequency table for the number of family members in a household:

Family size	$1 - 3$	$3 - 5$	$5 - 7$	$7 - 9$	$9 - 11$
Number of families	$7$	$8$	$2$	$2$	$1$

Find the mode of this data.

HARD

IMPORTANT

Mathematics>Statistics>Measures of Central Tendency> Q 7

What are the properties of Mode.

Find the mode of the following distribution:

Height (in $cm$ )	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$	$80 - 90$
Number of plants	$4$	$3$	$8$	$11$	$6$	$2$

HARD

IMPORTANT

Mathematics>Statistics>Measures of Central Tendency> Q 8

What are the merits and demerits of median. Calculate the median from the following distribution:

Class:	$5 - 10$	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$	$30 - 35$	$35 - 40$	$40 - 45$
Frequency:	$5$	$6$	$15$	$10$	$5$	$4$	$2$	$2$

MEDIUM

IMPORTANT

Mathematics>Statistics>Measures of Central Tendency> Q 9

What are the merits and demerits of mean. Also find the mean of the following distribution:

$x$ :	$10$	$30$	$50$	$70$	$89$
$f$ :	$7$	$8$	$10$	$15$	$10$

MEDIUM

IMPORTANT

Mathematics>Statistics>Measures of Central Tendency> Q 10

What are the merits and demerits of mean. Following table shows the weight of $12$ students:

Weight (in $kgs$ ):	$67$	$70$	$72$	$73$	$75$
Number of students:	$4$	$3$	$2$	$2$	$1$

Find the mean weight of the students.

MEDIUM

IMPORTANT

Mathematics>Statistics>Measures of Central Tendency> Q 11

What are the merits and demerits of mean. Also find the mean of the following distribution:

$x$ :	$4$	$6$	$9$	$10$	$15$
$f$ :	$5$	$10$	$10$	$7$	$8$

EASY

IMPORTANT

Mathematics>Statistics>Measures of Central Tendency> Q 12

Identify the mode of $x$ and of $y$ in the following table.

$x$	$4$	$5$	$6$	$7$	$8$
$f$	$2$	$5$	$5$	$4$	$7$

$y$	$4$	$3$	$2$	$1$	$0$
$f$	$27$	$28$	$29$	$27$	$25$

EASY

IMPORTANT

Mathematics>Statistics>Measures of Central Tendency> Q 13

Identify the mode of $x$ and of $y$ in the following table.

$x$	$4$	$5$	$6$	$7$	$8$
$f$	$2$	$5$	$5$	$6$	$4$

$y$	$4$	$3$	$2$	$1$	$0$
$f$	$27$	$28$	$29$	$27$	$25$

EASY

IMPORTANT

Mathematics>Statistics>Measures of Central Tendency> Q 14

Identify the mode of $s$ and of $t$ in the following table.

$s$	$4$	$5$	$6$	$7$	$8$
$f$	$1$	$4$	$5$	$6$	$4$

$t$	$4$	$3$	$2$	$1$	$0$
$f$	$27$	$27$	$29$	$27$	$25$

EASY

IMPORTANT

Mathematics>Statistics>Measures of Central Tendency> Q 15

Identify the mode of $x$ and of $y$ in the following table.

$x$	$4$	$5$	$6$	$7$	$8$
$f$	$1$	$5$	$5$	$6$	$4$

$y$	$4$	$3$	$2$	$1$	$0$
$f$	$27$	$28$	$29$	$27$	$25$

MEDIUM

IMPORTANT

Mathematics>Statistics>Measures of Central Tendency> Q 16

The marks obtained in English test by $17$ students were recorded. What is the median marks of the students?

$\begin{array}{l} Marks out of 50 & Frequency & Cumulative frequency \\ 0 - 10 & 1 & 1 \\ 10 - 20 & 4 & 5 \\ 20 - 30 & 5 & 10 \\ 30 - 40 & 4 & 14 \\ 40 - 50 & 1 & 15 \end{array}$

MEDIUM

IMPORTANT

Mathematics>Statistics>Measures of Central Tendency> Q 17

The marks obtained in English test by $17$ students were recorded. What is the median marks of the students?

$\begin{array}{l} Marks out of 50 & Frequency & Cumulative frequency \\ 0 - 10 & 2 & 2 \\ 10 - 20 & 4 & 6 \\ 20 - 30 & 5 & 11 \\ 30 - 40 & 4 & 15 \\ 40 - 50 & 2 & 17 \end{array}$

EASY

IMPORTANT

Mathematics>Statistics>Measures of Central Tendency> Q 18

Find the median for the values of $t$ in the following table:

$t$	$4$	$5$	$6$	$7$	$8$
$f$	$14$	$10$	$4$	$12$	$15$

EASY

IMPORTANT

Mathematics>Statistics>Measures of Central Tendency> Q 19

Find the cumulative frequencies, and median for the values of $t$ in the following table:

$t$	$4$	$5$	$6$	$7$	$8$
$f$	$14$	$13$	$4$	$12$	$15$

MEDIUM

IMPORTANT

Mathematics>Statistics>Measures of Central Tendency> Q 20

If the mode is $34.5$ , then find the missing frequency?

Class	Frequency
$0 - 10$	$4$
$10 - 20$	$8$
$20 - 30$	$10$
$30 - 40$	$x$
$40 - 50$	$8$

Measures of Central Tendency

Measures of Central Tendency: Overview

Important Questions on Measures of Central Tendency

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