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 |
= 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
= Size of
50th item lies in 65th cumulative frequency and the corresponding median class is 15-20.
= 15 + (100/2−35)/30 × 5
= 15 + (50-35)/30 × 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 (₹) | 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 (₹) | 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
Here, l1 = 15, f1 = 30, f0 = 15, f2 = 20, i = 5
Substituting the values, we get,
Z = 15 + (30-15) / 2×30 – 15-20 × 5
= 15 + 15/ 60-35 × 5
= 15 + 15/25 × 5
=15 + 75/25
= 15+3=18
Thus, Mode = 18
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Nice
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