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Question
Solve the following :
Calculate of Q3, D5, and P35 for the given data
| Income (in lakhs ₹) | 1 | 2 | 3 | 4 | 5 | 6 | |
| No. of family | 2 | 5 | 20 | 25 | 15 | 12 | |
Solution
Arrange the data of the income in ascending order.
(i.e. from lowest number to highest as shown below) and the out the cumulative frequency.
| Income (in lakhs RS) | no. of family | cumulative frequency(cf) |
| 1 | 2 | 2 |
| 2 | 5 | 7 |
| 3 | 20 | 27 |
| 4 | 25 | 52 |
| 5 | 15 | 67 |
| 6 | 12 | 79 |
| N = 79 |
Q3 = Size of 3`((n +1)/4)^"th observation"`
= size of 3`((79+1)/4)^"th observation"`
= size of 3`(80/4)^"th observation"`
= size of 3 `(20)^"th observation"`
= size of 60th observation lies in cf 67
Hence, quartile value = Rs .5 lakhs Q3 = Rs. 5 Lakhs
D5 = size of 5`((n+1)/10)^"th observation"`
=size of 5`((79+1)/10)^"th observation"`
= size of 5`(80/10)^"th observation"`
= size of 5`(8)^"th observation"`
= size of `(40)^"th observation"`
Size of 40th observation lies in cf 52 , hence decile value =Rs. 4 Lakhs
D5 =Rs. 4 Lakhs
P35 =Size of 35`((n +1)/100)^"th observation"`
P35 =Size of 35`((79 +1)/100)^"th observation"`
P35 =Size of 35`(80/100)^"th observation"`
=Size of 35 `(0.80)^"th observation"`
=Size of 28th observation lies in cf 52
Hence, percentile value = Rs.4 lakhs P35 = Rs. 4 lakhs.
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RELATED QUESTIONS
Give the correct option:
Statements related to partition values that are correct.
- Exact divisions of percentiles into 100 parts gives 99 points
- Deciles have total 9 parts
- Quartiles are shown by Q1, Q2 and Q3
- symbolically, percentiles and Deciles are shown by P and D
Choose the correct pair:
| Group A | Group B |
| 1) Quartiles | a) Dj = size of j`((n + 1)/10) ^"th Observation"` |
| 2) Deciles | b) `"P"_k = l +(((kn)/100 – cf)/f) xx "h"` |
| 3) Percentiles | c) `"Q"_i = l +((("in")/4 – cf)/f) xx "h"` |
Give economic term:
Procedure for dividing the data into equal parts.
State with reasons whether you agree or disagree with the following statement:
Partition values have application only in theory but not in practice.
State with reasons whether you agree or disagree with the following statement:
Average can misinterpret the representative value.
Solve the following:
Calculate Q1, D4, and P26 for the following data.
| 18, 24, 45, 29, 4, 7, 28, 49, 16, 26, 25, 12, 10, 9, 8 |
A company produces tables which are packed in batches of 100. An analysis of the defective tubes in different batches has received the following information:
| No. of defective tubes | Less than 5 | 5 – 9 | 10 – 14 | 15 – 9 | 20 – 24 | 25 – 29 | 30 and above |
| No. of tubes | 45 | 51 | 84 | 39 | 20 | 8 | 4 |
Estimate the number of defective tubes in the central batch.
