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प्रश्न
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.
उत्तर
To find the number of defective tubes in the central batch, we have to find Q2.
Since, the given data is not continuous, we have to convert it in the continuous form by subtracting 0.5 from the lower limit and adding 0.5 to the upper limit of every class interval.
∴ the class intervals will be
Less than 4.5, 4.5 – 9.5, etc.
We construct the less than cumulative frequency table as given below:
| No. of defective tubes | No. of tubes (f) |
Less than cumulative frequency (c.f.) |
| Less than 4.5 | 45 | 45 |
| 4.5 – 9.5 | 51 | 96 |
| 9.5 – 14.5 | 84 | 180 ← Q2 |
| 14.5 – 19.5 | 39 | 219 |
| 19.5 – 24.5 | 20 | 239 |
| 24.5 – 29.5 | 8 | 247 |
| 29.5 and above | 4 | 251 |
| Total | 251 |
Here, N = 251
Q2 class = class containing `((2"N")/4)^"th"` observation
∴ `(2"N")/4=(2xx251)/4` = 125.5
Cumulative frequency which is just greater than (or equal to) 125.5 is 180.
∴ Q2 lies in the class 9.5 – 14.5
∴ L = 9.5, h = 5, f = 84, c.f. = 96
∴ Q2 = `"L" "h"/"f"((2"N")/4-"c.f.")`
= `9.5 + 5/84 (125.5 - 96)`
= `9.5 + 5/84 xx 29.5`
= `9.5 + (147.5)/84`
= 9.5 + 1.76
= 11.26
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संबंधित प्रश्न
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 |
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 | |
