# Sandeep Garg Solutions Class 11 Economics Chapter 5 - Measures of Central Tendency- Arithmetic Mean

Sandeep Garg Class 11 Economics Solutions Chapter 5 Measures of Central Tendency: Arithmetic Mean is illustrated by the professional economics educators from the contemporary edition of Sandeep Garg Economics Class 11 textbook solutions.

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## Sandeep Garg Solutions Class 11 – Chapter 5

Question 1

Find the average from the following data:

 3 5 7 9 11 13 17 19 20 21

Here, the average is calculated using a direct method.

$$\begin{array}{l}\left ( \bar{X} \right ) =\, \frac{EX}{N}\end{array}$$

$$\begin{array}{l}\bar{X}\, =\, \frac{3+5+7+9+11+13+17+19+20+21}{10}\end{array}$$

$$\begin{array}{l}\bar{X}\, =\, \frac{125}{10}\end{array}$$

$$\begin{array}{l}\bar{X}\, =\, 12.5\end{array}$$

Question 2

Following are the daily income of ten families. Evaluate the average daily income.

 S. No. 1 2 3 4 5 6 7 8 9 10 Daily Income 100 120 80 85 95 130 200 250 225 275

 S.No. Daily Income (in Rs.) (X) 1 2 3 4 5 6 7 8 9 10 80 100 90 80 90 110 190 230 210 250 N =10 âˆ‘X= 1430
$$\begin{array}{l}\left ( \bar{X} \right )\, =\, \frac{\sum X}{N}\end{array}$$

$$\begin{array}{l}\bar{X}\, =\, \frac{80+100+90+80+90+110+190+230+210+255}{10}\end{array}$$

$$\begin{array}{l}\bar{X}\, =\, \frac{1430}{10}\end{array}$$

$$\begin{array}{l}\bar{X}\, =\, 143\end{array}$$

Question 3

Find the average from the series.

 X 2 4 5 8 9 f 3 6 3 7 10

 X f fX 2 4 5 8 9 3 6 3 7 10 6 24 15 56 90 N=Î£f= 29 Î£fX= 191
$$\begin{array}{l}\bar{X}\, =\, \frac{\sum fX}{\sum f}\end{array}$$

$$\begin{array}{l}\bar{X}\, =\, \frac{191}{29}\end{array}$$

$$\begin{array}{l}\bar{X}\, =\, 6.59\end{array}$$

The average of the given series is 6.59.

Question 4

Find the arithmetic mean from the frequency table.

 Height (in cm) 55 58 60 62 64 65 Number of Flowers 10 12 18 12 10 7

 Height (X) Flowers (f) fX 55 58 60 62 64 65 10 12 18 12 10 7 550 696 1080 744 640 455 N=Î£f= 69 Î£fX=4165
$$\begin{array}{l}\bar{X}\, =\, \frac{\sum fX}{\sum f}\end{array}$$

Or,

$$\begin{array}{l}\bar{X}\, =\, \frac{3265}{69}\end{array}$$

$$\begin{array}{l}\bar{X}\, =\, 60.37\end{array}$$

Question 5

From the following data arrange the mean marks acquired by the students using the direct method.

 Marks 0âˆ’4 4âˆ’8 8âˆ’12 12âˆ’16 16âˆ’20 20âˆ’24 No. of Students 7 9 16 8 6 4

 Class Interval (Marks) Mid-Values (m) Students (f) fm 0 âˆ’ 4 4 âˆ’ 8 8 âˆ’ 12 12 âˆ’ 16 16 âˆ’ 20 20 âˆ’ 24 2 6 10 14 18 22 7 9 16 8 6 4 14 54 160 112 108 88 Î£f Î£f=50 Î£fm Î£fm=586
$$\begin{array}{l}\bar{X}\, \frac{\sum fm}{\sum f}\end{array}$$

$$\begin{array}{l}\bar{X}\, =\, \frac{536}{50}\end{array}$$

$$\begin{array}{l}\bar{X}\, =\, 10.72\end{array}$$

The mean marks acquired by the students are 10.72

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