If the arithmetic mean of the data given below is 28 , find ( a ) The missing frequency and ( b ) The median of the series. Profit per retail shop (in ₹ ) 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 Number of retail shops 12 18 27 - 17 6

( a ) Let the missing frequency be f 1 . Arithmetic Mean = 28 Profit Per Retail Shop (in ₹) Class Interval Number of Retail Shops ( f ) Mid Value ( m ) f m 0 - 10 12 5 60 10 - 20 18 15 270 20 - 30 27 25 675 30 - 40 f 1 35 35 f 1 40 - 50 17 45 765 50 - 60 6 55 330 Σ f = 80 + f 1 Σ f m = 2100 + 35 f 1 X ¯ = Σ f m Σ f or 28 = 2100 + 35 f 1 80 + f 1 or 2240 + 28 f 1 = 2100 + 35 f or 2240 - 2100 = 35 f 1 - 28 f 1 or 140 = 7 f 1 f 1 = 20 Hence, the missing frequency is 20 . ( b ) Class Interval Frequency Cumulative Frequency 0 - 10 12 12 10 - 20 18 30 20 - 30 27 57 30 - 40 20 77 40 - 50 17 94 50 - 60 6 100 Total Σ f = 100 So, the Median class = Size of N 2 t h item = 50 t h term. 50 t h item lies in the 57 t h cumulative frequency and the corresponding class interval is 20 - 30 Median = L + N 2 - C F f × i = 20 + 100 2 - 30 27 × 10 = 20 + 50 - 30 27 × 10 = 20 + 20 27 × 10 = 27 . 40

The following table gives the daily income of ten workers in a factory. Find the arithmetic mean. Workers A B C D E F G H I J Daily Income (in ₹ ) 120 150 180 200 250 300 220 350 370 260

Workers Daily Income (in ₹ ) ( X ) A 120 B 150 C 180 D 200 E 250 F 300 G 220 H 350 I 370 J 260 Total Σ X = 2400 N = 10 X ¯ = Σ X N = 2400 10 = 240 Arithmetic mean is the most commonly used measure of central tendency. It is defined as the sum of the values of all observations divided by the number of observations.

E M B I B E

Statistics for Economics>Chapter 5 - Measures of Central Tendency>Q 22

EASY

11th CBSE

IMPORTANT

Earn 100

Which average is affected most by the presence of extreme items?

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Important Questions on Measures of Central Tendency

EASY

11th CBSE

IMPORTANT

Statistics for Economics>Chapter 5 - Measures of Central Tendency>Q 23

The algebraic sum of deviation of a set of

n

values from

A . M .

is,

EASY

11th CBSE

IMPORTANT

Statistics for Economics>Chapter 5 - Measures of Central Tendency>Q 24

The sum of deviation of items from the median is zero.

EASY

11th CBSE

IMPORTANT

Statistics for Economics>Chapter 5 - Measures of Central Tendency>Q 25

An average alone is not enough to compare series.

EASY

11th CBSE

IMPORTANT

Statistics for Economics>Chapter 5 - Measures of Central Tendency>Q 26

Arithmetic mean is a positional value.

EASY

11th CBSE

IMPORTANT

Statistics for Economics>Chapter 5 - Measures of Central Tendency>Q 27

The upper quartile is the lowest value of top

25 %

of items.

EASY

11th CBSE

IMPORTANT

Statistics for Economics>Chapter 5 - Measures of Central Tendency>Q 28

Median is unduly affected by extreme observations.

HARD

11th CBSE

IMPORTANT

Statistics for Economics>Chapter 5 - Measures of Central Tendency>Q 29

If the arithmetic mean of the data given below is

28,

find

(a)

The missing frequency and

(b)

The median of the series.

Profit per retail shop (in $₹$ )	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$
Number of retail shops	$12$	$18$	$27$	$-$	$17$	$6$

HARD

11th CBSE

IMPORTANT

Statistics for Economics>Chapter 5 - Measures of Central Tendency>Q 30

The following table gives the daily income of ten workers in a factory. Find the arithmetic mean.

Workers	$A$	$B$	$C$	$D$	$E$	$F$	$G$	$H$	$I$	$J$
Daily Income (in $₹$ )	$120$	$150$	$180$	$200$	$250$	$300$	$220$	$350$	$370$	$260$

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