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प्रश्न
Calculate all the quartiles for the following frequency distribution:
| No. of E-transactions per day | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| No. of days | 10 | 35 | 45 | 95 | 64 | 32 | 10 | 9 |
उत्तर
We construct the less than cumulative frequency table as given below:
| No. of E-transaction per day | No. of days | Less than cumulative frequency (c.f.) |
| 0 | 10 | 10 |
| 1 | 35 | 45 |
| 2 | 45 | 90 ← Q1 |
| 3 | 95 | 185 ← Q2 |
| 4 | 64 | 249 ← Q3 |
| 5 | 32 | 281 |
| 6 | 10 | 291 |
| 7 | 9 | 300 |
| Total | 300 |
Here, n = 300
Q1 = value of `(("n" + 1)/4)^"th"`observation
= value of `((300 + 1)/4)^"th"`observation
= value of (75.25)th observation
Cumulative frequency which is just greater than (or equal to) 75.25 is 90.
∴ Q1 = 2
Q2 = value of 2`(("n" + 1)/4)^"th"`observation
= value of 2`((300 + 1)/4)^"th"`observation
= value of (2 × 75.25)th observation
= value of (150.50)th observation
Cumulative frequency which is just greater than (or equal to) 150.50 is 185.
∴ Q2 = 3
Q3 = value of 3`(("n" + 1)/4)^"th"` observation
= value of 3`((300 + 1)/4)^"th"` observation
= value of (3 × 75.25)th observation
= value of (225.75)th observation
Cumulative frequency which is just greater than (or equal to) 225.75 is 249.
∴ Q3 = 4
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संबंधित प्रश्न
Give the correct option:
Statements that do not apply to Quartiles.
- First, arrange the values in ascending or descending order.
- Observation can be divided into 4 parts.
- They are represented as Q1, Q2 and Q3.
- Q2 is also known as a median.
Give economic term:
Value that divides the whole set of observations into four equal parts.
State with reasons whether you agree or disagree with the following statement:
Median is also known as the second quartile.
Calculate Q3 for the following data.
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| No. of firms | 20 | 30 | 70 | 48 | 32 | 50 |
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The heights (in cm) of 10 students are given below: 148, 171, 158, 151, 154, 159, 152, 163, 171, 145. Calculate Q1 and Q3 for above data.
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| 145 – 150 | 4 |
| 150 – 155 | 6 |
| 155 – 160 | 25 |
| 160 – 165 | 57 |
| 165 – 170 | 64 |
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| Wages more than (in ₹) |
No. of workers |
| 8000 | 160 |
| 9000 | 155 |
| 10000 | 137 |
| 11000 | 91 |
| 12000 | 57 |
| 13000 | 23 |
| 14000 | 10 |
| 15000 | 1 |
| 16000 | 0 |
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| No. of employees | 6 | 8 | 15 | 26 | 20 | 14 | 11 |
