Find median, lower quartile and upper quartile for the data set: Variate 15 18 20 22 25 27 30 Frequency 4 6 8 9 7 8 6

We construct the following table: Variate 15 18 20 22 25 27 30 Frequency 4 6 8 9 7 8 6 Cumulative frequency 4 10 18 27 34 42 48 Here , n = ∑ f i = 48 Median = n 2 th observation + n 2 + 1 th observation 2 = 24 th value + 25 th value 2 = 22 + 22 2 = 22 [Since both 24 th and 25 th values are same] Q 1 = Lower quartile = n + 1 4 th value = 48 + 1 4 th value i.e 12 . 25 th value = 12 th value + 0 . 25 13 th value - 12 th value = 20 + 0 . 25 20 - 20 = 20 ∴ Q 1 = 20 Upper quartile = Q 3 = 3 n + 1 4 th value = 3 48 + 1 4 th value = 36 . 75 th value = 36 th value + 0 . 75 37 th value - 36 th value = 27 + 0 . 75 27 - 27 = 27 Hence, the median, lower quartile and upper quartile are 22 , 20 and 27

Find median, lower quartile and upper quartile for the data set: Variate 25 31 34 40 45 48 50 60 Frequency 3 8 10 15 10 9 9 2

We construct the following table: Variate 25 31 34 40 45 48 50 60 Frequency 3 8 10 15 10 9 6 2 Cumulative frequency 3 11 21 36 46 55 61 63 Here, n = ∑ f i = 63 (odd) Median = n + 1 2 th observations = 63 + 1 2 th observations i.e. 32 th observations = 40 Q 1 = Lower quartile = n + 1 4 th value = 63 + 1 4 th value i.e 16 th value = 34 ∴ Q 1 = 34 Upper quartile = Q 3 = 3 n + 1 4 th value = 3 63 + 1 4 th value = 48 th value = 48 Hence, the median, lower quartile and upper quartile are 40 , 34 and 48 .

Find Q 1 , Q 3 , D 6 and P 45 for the following data: x i 18 19 20 21 22 23 24 25 26 27 f i 15 18 25 27 40 25 19 16 8 7

We construct the following table : x i 18 19 20 21 22 23 24 25 26 27 f i 15 18 25 27 40 25 19 16 8 7 Cumulative frequency 15 33 58 85 125 150 169 185 193 200 Here, n = ∑ f i = 200 Q 1 = n + 1 4 th value = 200 + 1 4 th value = 50 . 25 th value = 50 th value + 0 . 25 51 th - 50 th value = 20 + 0 . 25 20 - 20 = 20 Q 3 = 3 n + 1 4 th value = 3 200 + 1 4 th value = 150 . 75 th value = 120 th value + 0 . 75 151 th - 150 th value = 23 + 0 . 75 24 - 23 = 23 . 75 D 6 = 6 n + 1 10 th value = 6 200 + 1 10 th value = 120 . 6 th value = 120 th value + 0 . 6 121 th - 120 th value = 22 + 0 . 6 22 - 22 = 22 P 45 = 45 n + 1 100 th value = 45 200 + 1 100 th value = 90 . 45 th value = 90 th value + 0 . 45 91 th - 90 th value = 22 + 0 . 45 22 - 22 = 22 Hence, the partition values of Q 1 , Q 3 , D 6 and P 45 are 20 , 23 . 75 , 22 and 22 .

For the following data, compute lower and upper quartiles, P 90 and P 5 . Marks Below 10 10 - 20 20 - 40 40 - 60 60 - 80 Above 80 Number of students 8 10 22 25 10 5

We construct the following table : Marks 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 80 - 90 Number of students 8 10 11 11 12 . 5 12 . 5 5 5 5 Cumulative frequency 8 18 29 40 52 . 5 65 70 75 80 Here, n = ∑ f i = 80 Lower quartile is the n 4 th value i.e 20 th value which lies in the class 20 - 30 . ∴ l = 20 ; c = 18 ; f = 11 ; i = 10 Thus, Q 1 = l + n 4 - c f × i = 20 + 20 - 18 11 × 10 = 20 + 20 11 ⇒ Q 1 = 21 . 82 Upper quartile Q 3 is the 3 n 4 th value i.e 60 th value which lies in the class 50 - 60 . ∴ l = 50 ; c = 52 . 5 ; f = 12 . 5 ; i = 10 Thus, Q 3 = l + 3 n 4 - c f × i = 50 + 60 - 52 . 5 12 . 5 × 10 = 20 + 7 . 5 × 10 12 . 5 = 56 P 90 is the 90 n 100 th value i.e 90 × 80 100 th value i.e 72 th value which lies in the class 70 - 80 . ∴ l = 70 ; c = 70 ; f = 5 ; i = 10 Thus, P 90 = l + 90 n 100 - c f × i = 70 + 72 - 70 5 × 10 = 74 P 5 is the 5 n 100 th value i.e 5 × 80 100 th value i.e 4 th value which lies in the class 0 - 10 . ∴ l = 0 ; c = 0 ; f = 8 ; i = 10 Thus, P 5 = l + 5 n 100 - c f × i = 0 + 4 - 0 5 × 10 = 8

Calculate the interquartile range for the following data : Daily wages (in ₹) 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 No. of workers 22 38 46 35 20

We construct the table is as under : Daily wages (in ₹) 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 No. of workers 22 38 46 35 20 Cumulative frequency 22 60 106 141 161 Here, n = ∑ f i = 161 (odd) Lower quartile Q 1 is the n 4 th value i.e 161 4 th = 40 . 25 th value which lies in the class 40 - 50 . ∴ l = 40 ; c = 38 ; f = 22 ; i = 10 Thus, Q 1 = l + n 4 - c f × i = 40 + 40 . 25 - 22 38 × 10 = 40 + 4 . 8026 = 44 . 8026 Upper quartile Q 3 is the 3 n 4 th value i.e 3 × 161 4 th = 120 . 75 th value which lies in the class 60 - 70 . ∴ l = 60 ; c = 35 ; f = 106 ; i = 10 Thus, Q 3 = l + 3 n 4 - c f × i = 60 + 120 . 75 - 106 35 × 10 = 60 + 4 . 2143 = 64 . 2143 Hence, interquartile range = Q 3 - Q 1 = 64 . 2143 - 44 . 8026 = 19 . 41

Calculate all three quartiles for the following frequency distribution : Height ( in inches) 58 59 60 61 62 63 64 65 66 No. of students 15 20 32 35 35 22 20 10 8

We construct the cumulative frequency distribution table is as under : Height ( in inches) 58 59 60 61 62 63 64 65 66 No. of students 15 20 32 35 35 22 20 10 8 Cumulative frequency 15 35 67 102 137 159 179 189 197 ∴ Q 1 is the n + 1 4 th value i.e 197 + 1 4 th = 49 . 5 th value Thus, Q 1 = 60 [ since 49 th and 50 th values are same i.e 60 . ] Q 2 be the median = 2 n + 1 4 th value = 197 + 1 2 th value = 99 th value = 61 And Q 3 = 3 n + 1 4 th value = 3 197 + 1 4 th value 148 . 5 th = 63 . Hence, all the three quartiles are 60 , 61 and 63 .

HARD

11th ICSE

IMPORTANT

Earn 100

Find median, lower quartile and upper quartile for the following data sets:

$3, 6, 8, 13, 15, 5, 21, 23, 17, 10, 9, 1.20, 21, 18, 12$

Important Questions on Statistics

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 1 - Statistics>EXERCISE>Q 1

Find median, lower quartile and upper quartile for the data set:

Variate	$15$	$18$	$20$	$22$	$25$	$27$	$= Q_{3} = 3 {(\frac{n + 1}{4})}^{th} value = 3 {(\frac{16 + 1}{4})}^{th} value = 12 . 75^{th} value$
Frequency	$4$	$6$	$8$	$9$	$7$	$8$	$6$

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 1 - Statistics>EXERCISE>Q 1

Find median, lower quartile and upper quartile for the data set:

Variate	$25$	$31$	$34$	$40$	$45$	$48$	$50$	$60$
Frequency	$3$	$8$	$10$	$15$	$10$	$9$	$9$	$2$

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 1 - Statistics>EXERCISE>Q 2

Calculate the partition values

Q_{1}, Q_{2}, D_{2}, D_{7}, D_{8}, P_{22}

and

P_{38}

for the following data:

4, 7, 3, 9, 4, 12, 7, 12, 6, 18, 19, 20, 4, 7 . 6, 5, 17, 16 . 19

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 1 - Statistics>EXERCISE>Q 3

Calculate the $3^{rd}$ quartile $6^{th}$ decile and $70^{th}$ percentile for the following data :

$28, 17, 12, 25, 26, 19, 13, 27, 21, 16$ .

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 1 - Statistics>EXERCISE>Q 4

Find $Q_{1}, Q_{3}, D_{6}$ and $P_{45}$ for the following data:

$x_{i}$	$18$	$19$	$20$	$21$	$22$	$23$	$24$	$25$	$26$	$27$
$f_{i}$	$15$	$18$	$25$	$27$	$40$	$25$	$19$	$16$	$8$	$7$

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 1 - Statistics>EXERCISE>Q 5

For the following data, compute lower and upper quartiles, $P_{90}$ and $P_{5}$ .

Marks	Below $10$	$10 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	Above $80$
Number of students	$8$	$10$	$22$	$25$	$10$	$5$

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 1 - Statistics>EXERCISE>Q 6

Calculate the interquartile range for the following data :

Daily wages (in ₹)	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$
No. of workers	$22$	$38$	$46$	$35$	$20$

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 1 - Statistics>EXERCISE>Q 7

Calculate all three quartiles for the following frequency distribution :

Height ( in inches)	$58$	$59$	$60$	$61$	$62$	$63$	$64$	$65$	$66$
No. of students	$15$	$20$	$32$	$35$	$35$	$22$	$20$	$10$	$8$

Find median, lower quartile and upper quartile for the following data sets: 3, 6, 8, 13, 15, 5, 21, 23, 17, 10, 9, 1.20, 21, 18, 12

Important Questions on Statistics

Learn and Prepare for any exam you want !

Find median, lower quartile and upper quartile for the following data sets:

$3, 6, 8, 13, 15, 5, 21, 23, 17, 10, 9, 1.20, 21, 18, 12$