40 40 students enter for a game of shot-put competition. The distance thrown (in metres) is recorded below: Distance in m 12 - 13 13 - 14 14 - 15 15 - 16 16 - 17 17 - 18 18 - 19 Number of students 3 9 12 9 4 2 1 Use a graph paper to draw an ogive for the above distribution. Use a scale of 2 c m = 1 m on one axis and 2 c m = 5 students on the other axis. Hence using graph find Upper Quartile.

If we arrange the given data in cumulative frequency table, we get Distance m Number of students Less than Number of persons 12 - 13 3 12 0 13 - 14 9 13 3 14 - 15 12 14 12 15 - 16 9 15 24 16 - 17 4 16 33 17 - 18 2 17 37 18 - 19 1 18 39 N = 40 19 40 The upper or third quartile, denoted as Q 3 , is the central point that lies between the median and the highest number of the distribution. So, upper quartile = 3 4 ( n + 1 ) t h t e r m = 3 4 40 + 1 = 30 t h t e r m Thus, the upper quartile is 15 . 7

The weights of 60 boys are given in the following distribution table: Weight(kg) 37 38 39 40 41 No. of boys 10 14 18 12 6 Find: Inter-quartile range

Weight (kg)x no. of boys cumulative frequency 37 10 10 38 14 24 39 18 42 40 12 54 41 6 60 x / o . of terms = 60 Interquartile range:-When a data set has outliers, variability is often summarized by a statistic called the interquartile range, which is the difference between the first and third quartiles. The first quartile, denoted Q 1 , is the value in the data set that holds 25% of the values below it Q 3 - Q 1 = 40 - 38 = 2

The weights of 60 boys are given in the following distribution table: Weight(kg) 37 38 39 40 41 No. of boys 10 14 18 12 6 Find: Lower quartile

Weight (kg)x no. of boys cumulative frequency 37 10 10 38 14 24 39 18 42 40 12 54 41 6 60 x / o . of terms = 60 To find the lower quartile of a set of data, we can find the median of the data and then find the median of the first half. This strategy is similar to dividing a cake into halves, and then dividing one of the halves in half so that you end up with a quarter of the cake. Lower quartile ( Q , 1 ) = 60 4 term = 15 th term = 38

Compute all quartiles from the given data Weekly Income (in Rs.) Number of workers 58 2 59 3 60 6 61 15 62 10 63 5 64 4 65 3 66 1

Given, Weekly Income (in Rs.) Number of workers 58 2 59 3 60 6 61 15 62 10 63 5 64 4 65 3 66 1 The cumulative frequency of the table is given below: Weekly Income (in Rs.) Number of Workers Cumulative frequency 58 2 2 59 3 5 60 6 11 61 15 26 62 10 36 63 5 41 64 4 45 65 3 48 66 1 49 N = 49 Lower Quartile We have, N 4 = 49 4 = 12 . 25 The cumulative frequency just greater than N 4 is 26 and the corresponding value of the variable is 61 . Q 1 = R s . 61 Middle Quartile (median): We have N 2 = 49 2 = 24 . 5 The cumulative frequency just greater than N 2 is 26 and the corresponding value of the variable is 61 . Q 2 = Rs . 61 Upper Quartile: We have 3 N 4 = 3 × 49 4 = 36 . 75 The cumulative frequency just greater than 3 N 4 is 41 and the corresponding value of the variable is 63 . Q 3 = R s . 63 Hence, Q 1 = Rs . 61 , Q 2 = Rs . 61 , Q 3 = Rs . 63

The following distribution represents the height of 160 students of a school. Heights (in cm ) Number of Students. 140 - 145 12 145 - 150 20 150 - 155 30 155 - 160 38 160 - 165 24 165 - 170 16 170 - 175 12 175 - 180 8 Draw an ogive for the given distribution taking 2 cm = 5 cm of height on one axis and 2 cm = 20 students on the other axis. Using the graph, determine: the inter-quartile range.

Height ( cm ) No. of students Cumulative frequency 140 - 145 12 12 145 - 150 20 32 150 - 155 30 62 155 - 160 38 100 160 - 165 24 124 165 - 170 16 140 170 - 175 12 152 175 - 180 8 160 N = 160 No. of terms = 160 lkower quartile ( Q ) = 160 4 = 40 th = 152 Upper quatile ( Q 3 ) = 3 × 160 4 = 120 th term = 164 . Inner quartile range = Q 3 - Q 1 = 164 - 152 = 12

Find Median and Quartiles for the following data: Size Frequency Size Frequency 4 40 12 50 5 48 13 52 6 52 14 41 7 56 15 57 8 60 16 63 9 63 17 52 10 57 18 48 11 55 19 43

We know that Median = Q 2 . So, we have to find median , Q 1 , Q 3 . Given Data along with cummulative frequencies: Size Frequency Cummulative Frequency Size Frequency Cummulative Frequency 4 40 40 12 50 481 5 48 88 13 52 533 6 52 140 14 41 574 7 56 196 15 57 631 8 60 256 16 63 694 9 63 319 17 52 746 10 57 376 18 48 794 11 55 431 19 43 837 Total N = 837 N = ∑ f = 837 ⇒ N + 1 2 = 838 2 = 419 The cumulative frequency just greater than 419 is 431 . The size corresponding to 431 is 11 . Hence, the median size is 11 . Q 1 = N + 1 4 t h = 838 4 t h = 209 . 5 t h item The cumulative frequency just greater than 209 . 5 is 256 . The size corresponding to 256 is 8 . The first quartile size is 8 Q 3 = 3 ( N + 1 4 ) t h = 3 × 838 4 t h = 628 . 5 t h The cumulative frequency just greater than 628 . 5 is 631 . The size corresponding to 631 is 15 . The third quartile size is 15

The weights of 60 boys are given in the following distribution table: Weight(kg) 37 38 39 40 41 No. of boys 10 14 18 12 6 Find: Upper quartile

Weight (kg)x no. of boys cumulative frequency 37 10 10 38 14 24 39 18 42 40 12 54 41 6 60 x / o . of terms = 60 The upper quartile is the median of the upper half of a data set. This is located by dividing the data set with the median and then dividing the upper half that remains with the median again, this median of the upper half being the upper quartile Upper quartile ( Q 3 ) 3 × 60 th 4 term = 45 th term = 40

Write merits and demerits of Quartile Deviation

EASY

Mathematics>Statistics>Statistics>Further Partition Values

50^{th}

percentile is equal to __________

EASY

Mathematics>Statistics>Statistics>Further Partition Values

The probable value of mean deviation when

Q_{3} = 40

and

Q_{1} = 15

is

HARD

Mathematics>Statistics>Statistics>Further Partition Values

$40$ 40 students enter for a game of shot-put competition. The distance thrown (in metres) is recorded below:

Distance in $m$	$12 - 13$	$13 - 14$	$14 - 15$	$15 - 16$	$16 - 17$	$17 - 18$	$18 - 19$
Number of students	$3$	$9$	$12$	$9$	$4$	$2$	$1$

Use a graph paper to draw an ogive for the above distribution.

Use a scale of $2 c m = 1 m$ on one axis and $2 c m = 5$ students on the other axis. Hence using graph find Upper Quartile.

HARD

Mathematics>Statistics>Statistics>Further Partition Values

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

EASY

Mathematics>Statistics>Statistics>Further Partition Values

What percentage of values lies between $5^{t h}$ and $25^{t h}$ percentile?

EASY

Mathematics>Statistics>Statistics>Further Partition Values

The marks obtained by $19$ students of a class are given below:

$27, 36, 22, 31, 25, 26, 33, 24, 37, 32, 29, 28, 36, 35, 27, 26, 32, 35$ and $28$ . Find:

Lower quartile

MEDIUM

Mathematics>Statistics>Statistics>Further Partition Values

Julian and Aneesh are reading articles from different magazines . They count the numbers of words in a random selection of sentences from their articles and the result are recorded below:

Julian

(reading the Statistician) : $23 31 12 19 23 13 24$

Aneesh:

(reading the Algebraist): $19 12 13 16 18 15 18 21 22$

Calculate the interquartile range for each article.

MEDIUM

Mathematics>Statistics>Statistics>Further Partition Values

Calculate $D_{9}$ from the following frequency distribution

$x$	$58$	$59$	$60$	$61$	$62$	$63$	$64$	$65$	$66$
$f$	$2$	$3$	$6$	$15$	$10$	$5$	$4$	$3$	$2$

MEDIUM

Mathematics>Statistics>Statistics>Further Partition Values

The weights of

60

boys are given in the following distribution table:

Weight(kg)	$37$	$38$	$39$	$40$	$41$
No. of boys	$10$	$14$	$18$	$12$	$6$

Find:

Inter-quartile range

HARD

Mathematics>Statistics>Statistics>Further Partition Values

The marks obtained by

19

students of a class are given below:

$27, 36, 22, 31, 25, 26, 33, 24, 37, 32, 29, 28, 36, 35, 27, 26, 32, 35$ and $28$ . Find:

Interquartile range.

MEDIUM

Mathematics>Statistics>Statistics>Further Partition Values

The weights of

60

boys are given in the following distribution table:

Weight(kg)	$37$	$38$	$39$	$40$	$41$
No. of boys	$10$	$14$	$18$	$12$	$6$

Find:

Lower quartile

EASY

Mathematics>Statistics>Statistics>Further Partition Values

Second quartile and _____ deciles are equal.

EASY

Mathematics>Statistics>Statistics>Further Partition Values

The marks obtained by

19

students of a class are given below:

$27, 36, 22, 31, 25, 26, 33, 24, 37, 32, 29, 28, 36, 35, 27, 26, 32, 35$ and $28$ . Find:

Upper quartile

HARD

Mathematics>Statistics>Statistics>Further Partition Values

Compute all quartiles from the given data

Weekly Income (in Rs.)	Number of workers
$58$	$2$
$59$	$3$
$60$	$6$
$61$	$15$
$62$	$10$
$63$	$5$
$64$	$4$
$65$	$3$
$66$	$1$

MEDIUM

Mathematics>Statistics>Statistics>Further Partition Values

The following distribution represents the height of $160$ students of a school.

Heights (in $cm$ )	Number of Students.
$140 - 145$	$12$
$145 - 150$	$20$
$150 - 155$	$30$
$155 - 160$	$38$
$160 - 165$	$24$
$165 - 170$	$16$
$170 - 175$	$12$
$175 - 180$	$8$

Draw an ogive for the given distribution taking $2 cm = 5 cm$ of height on one axis and $2 cm = 20$ students on the other axis. Using the graph, determine:

the inter-quartile range.

MEDIUM

Mathematics>Statistics>Statistics>Further Partition Values

From the following data; Find:

Upper quartile

$25, 10, 40, 88, 45, 60, 77, 36, 18, 95, 56, 65, 7, 0, 38$ and $83$