T.R. Jain and V.K. Ohri Solutions for Class 11 Statistics Economics Chapter 10 : Measures of Central Tendency - Median and Mode

This chapter is regarded as an important concept to be studied thoroughly by the students. Here, we have provided T.R. Jain and V.K. Ohri Solutions for Class 11.

 Board CBSE Class Class 11 Subject Statistics for Economics Chapter Chapter 10 Chapter Name Measures of Central Tendency- Median and Mode Number of questions solved 04 Category T.R. Jain and V.K. Ohri

This chapter covers the following concepts:

• Â  Â  Â  Median
• Â  Â  Â  Finding the median value
• Â  Â  Â  Missing frequency
• Â  Â  Â  Graphic determination of the median
• Â  Â  Â  Partition value: Quartile

T.R. Jain and V.K. Ohri Solutions for Class 11 Statistics Economics Chapter 10 – Measures of Central Tendency- Median and Mode

Question 1

The following series shows the marks of nine students of Class 11 in statistics. Find the median marks.

 Marks 22 16 18 13 15 19 17 20 23

Solution:

The data is first arranged in the ascending order:

 S.no. Marks 1 13 2 15 3 16 4 17 5 18 6 19 7 20 8 22 9 23 N = 9
$$\begin{array}{l}M\, =\, Size\, of\,\left (\frac{N\,+ 1}{2} \right)th\, item\end{array}$$
$$\begin{array}{l}=\, Size\, of\, \left (\frac{9\, +\, 1}{2} \right)th\, item\end{array}$$

= Size of 5th item = 18

Hence, Median = 18

Question 2

The following table gives the marks obtained by some students. Calculate the median marks.

 Marks 0-5 5-10 10-15 15-20 20-25 25-30 30-35 35-40 40-45 Number of students 6 12 17 30 10 10 8 5 2

Solution:

 Marks Frequency (f) Cumulative Frequency 0-5 6 6 5-10 12 18 10-15 17 35(c.f.) (l1)15-20 30 (f) 65 20-25 10 75 25-30 10 85 30-35 8 93 35-40 5 98 40-45 2 100 = N = 100

M = Size of

$$\begin{array}{l}\left (\frac{N}{2}\right)th\, item\end{array}$$

= Size of

$$\begin{array}{l}\left (\frac{100}{2}\right)th\, item\end{array}$$
= Size of 50th item

50th item lies in 65th cumulative frequency and the corresponding median class is 15-20.

$$\begin{array}{l}M = l1\, +\, \frac{N/2\, -\, c.f.}{f}\times i\end{array}$$

= 15 + (100/2âˆ’35)/30 Ã— 5

= 15 + (50-35)/30 Ã— 5

= 15 + 5/2

= 15 + 2.5

=17.5

Median = 17.5 marks

Question 3

Find the mode from the following data:

8, 10, 5, 8, 12, 7, 8, 9, 11, 7

Solution:

Arrange the series in an ascending order as:

5, 7, 7, 8, 8, 8, 9, 10, 11, 12

After observing the series, we see that the value 8 occurs most frequently in the series.

Hence, Mode (Z) = 8

Question 4

Calculate the mode from the following data:

 Wages (â‚¹) 0-5 5-10 10-15 15-20 20-25 25-30 30-35 Number of workers 3 7 15 30 20 10 5

Solution:

 Wages (â‚¹) Frequency (f) 0-5 3 5-10 7 10-15 15 (f0) (ll) 15-20 30 (f1) 20-25 20 (f2) 25-30 10 30-35 5

Since the series is regular, we may not do grouping for the location of the model group. By inspection, the modal class is 15-20.

Z = l1

$$\begin{array}{l}+\, \frac{f1-f0}{2f1\, -\, f0\,- f2}\times i\end{array}$$

Here, l1 = 15, f1 = 30, f0 = 15, f2 = 20, i = 5

Substituting the values, we get,

Z = 15 + (30-15) / 2Ã—30 – 15-20Â Ã— 5

= 15 + 15/ 60-35Â Ã— 5

= 15 + 15/25Â Ã— 5

=15 + 75/25

= 15+3=18

Thus, Mode = 18

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