In worksheet on finding the quartiles and the interquartile range of raw and arrayed data we will solve various types of practice questions on measures of central tendency. Here you will get 5 different types of questions on finding the quartiles and the interquartile range of raw and arrayed data.

**1.** The number of problems worked out by a student on
seven days of a week were following.

5, 9, 15, 11, 13, 17, 7

Find the (i) lower quartile, (ii) upper quartile, (iii) interquartile range, (iv) semi-interquartile range, and (v) range for the distribution.

**2.** Find the (i) lower quartile, (ii) upper quartile, and (iii) interquartile range for the following data.

2, 1, 0, 3, 1, 2, 3, 4, 3, 5

**3.** Find for the given distribution.

(i) the lower quartile, (ii) the upper quartile, and (iii) the interquartile range.

**Variate**

1

2

3

4

5

6

7

8

**Frequency**

8

1

7

15

11

6

10

5

**4.** Find for the given distribution.

(i) the lower quartile, (ii) the upper quartile, and (iii) the interquartile range.

**Hint:** Arrange the variates in ascending order.

**Variate**

30

40

10

20

50

60

**Frequency**

11

30

15

8

12

9

**5.** Find for the given distribution.

(i) the lower quartile, (ii) the upper quartile, and (iii) the interquartile range.

**Variate**

5

10

20

30

50

60

80

**Cumulative Frequency**

7

12

21

35

42

50

56

**Hint:** Here \(\frac{3N}{4}\) = \(\frac{3 × 56}{4}\) = 42 = cumulative frequency of the variate 50. So, Q3 = \(\frac{50 + 60}{2}\).

Answers on Worksheet on Finding the quartiles and the interquartile range of raw and arrayed data are given below to check the exact answers of the questions.

**Answers**

**1.** (i) 7

(ii) 15

(iii) 8

(iv) 4

(v) 12

**2.** (i) 1

(ii) 3

(iii) 2

3. (i) 3

(ii) 7

(iii) 4

**4.** (i) 20

(ii) 40

(iii) 20

**5.** (i) 20

(ii) 55

(iii) 35

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