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

E M B I B E

Statistics for Economics>Chapter 5 - Measures of Central Tendency>Q 21

EASY

11th CBSE

IMPORTANT

Earn 100

The most suitable average for qualitative measurement is

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Important Questions on Measures of Central Tendency

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11th CBSE

IMPORTANT

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

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

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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,

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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.

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11th CBSE

IMPORTANT

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

An average alone is not enough to compare series.

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11th CBSE

IMPORTANT

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

Arithmetic mean is a positional value.

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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.

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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	$12$	$18$	$27$	$-$	$17$	$6$

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