Quartiles

Q.

Question 7
The runs scored by two teams A and B on the first 60 balls in a cricket match are given below:
$\begin{array}{ccc}\text{Number of balls}& \text{Team A}& \text{Team B}\\ 1-6& 2& 5\\ 7-12& 1& 6\\ 13-18& 8& 2\\ 19-24& 9& 10\\ 25-30& 4& 5\\ 31-36& 5& 6\\ 37-42& 6& 3\\ 43-48& 10& 4\\ 49-54& 6& 8\\ 55-60& 2& 10\end{array}$
Represent the data of both the teams on the same graph by frequency polygons.

Q. We can find the quartiles from the ogive for grouped data. Here the y-axis of the ogive represents _________.

1. frequency
2. class-interval
3. class mark
4. cumulative frequencies

Q. Using the frequency distribution table given below, draw 'less than ogive'. Then from the ogive, find: [6 MARKS]
i) lower quartile
ii) upper quartile
iii) semi-interquartile range
$\begin{array}{cc}Classinterval& Frequency\\ 5-10& 3\\ 10-15& 4\\ 15-20& 6\\ 20-25& 9\\ 25-30& 7\\ 30-35& 1\end{array}$

Q.

The weight of 50 workers is given below:

$\begin{array}{cccccccc}Weightinkg& 50-60& 60-70& 70-80& 80-90& 90-100& 100-110& 110-120\\ Numberofworkers& 4& 7& 11& 14& 6& 5& 3\end{array}$

Draw an ogive of the given distribution using a graph sheet. Take 2 cm = 10 kg on one axis and 2 cm = 5 workers along the other axis. Use a graph to estimate the upper and lower quartiles.

1. Q₁ = 79.1, Q₃ = 96

2. Q₁ = 79.1, Q₃ = 95.1

3. Q₁ = 79.1, Q₃ = 91.1

4. Q₁ = 71.1, Q₃ = 91.1

Q.

Find the inter-quartile range for the following data:

3, 11, 32, 8, 14, 1, 10, 27, 22, 4, 30

1. 24

2. 4

3. 27

4. 23

Q.

The given table shows the Marks obtained by students in Mathematics.

$\begin{array}{cc}\text{Marks}& \text{No. of Students}\\ 0-10& 3\\ 10-20& 7\\ 20-30& 12\\ 30-40& 15\\ 40-50& 20\\ 50-60& 9\\ 60-70& 8\\ 70-80& 16\\ 80-90& 14\\ 90-100& 6\end{array}$

Using the table determine the Number of students who got above 74 % by drawing an ogive curve.

1. 25

2. 28

3. 30

4. 33

Q. For the given set of numbers, the lower quartile, the upper quartile and inter quartile range is
2, 4, 13, 14, 19, 20, 27

1. 4, 20, 16
2. 13, 20, 7
3. 2, 27, 25
4. 4, 27, 25

Q.

The table shows the Distribution of the Scores obtained by 155 shooters in a shooting competition.

$\begin{array}{cc}\text{Scores}& \text{No. of shooters}\\ 0-10& 10\\ 10-20& 12\\ 20-30& 15\\ 30-40& 8\\ 40-50& 20\\ 50-60& 24\\ 60-70& 7\\ 70-80& 11\\ 80-90& 30\\ 90-100& 18\end{array}$

Use a graph sheet to draw the Histogram for the distribution.

The mode as seen in the graph is ___

Q.

The given table shows the Marks obtained by students in Mathematics.

$\begin{array}{cc}\text{Marks}& \text{No. of Students}\\ 0-10& 3\\ 10-20& 7\\ 20-30& 12\\ 30-40& 15\\ 40-50& 20\\ 50-60& 9\\ 60-70& 8\\ 70-80& 16\\ 80-90& 14\\ 90-100& 6\end{array}$

Using the table determine the Upper Quartile by drawing an ogive curve.

1. 80

2. 72

3. 76

4. 78

Q. Find the mean of following distribution with step-deviation method to the nearest integer

Class	10 - 15	15 - 20	20 - 25	25 - 30	30 - 35	35 - 40
Frequency	5	6	8	12	6	3

Q. We can find the quartiles from the ogive for grouped data. Here the y-axis of the ogive represents _________.

1. class mark
2. frequency
3. cumulative frequencies
4. class-interval

Q.

For the given set of numbers, the lower quartile, the upper quartile and inter quartile range is
2, 4, 13, 14, 19, 20, 27

1. 4, 27, 23

2. 13, 20, 7

3. 2, 27, 25

4. 4, 27, 25

Q.

The given table shows the Marks obtained by students in Mathematics.

$\begin{array}{cc}\text{Marks}& \text{No. of Students}\\ 0-10& 3\\ 10-20& 7\\ 20-30& 12\\ 30-40& 15\\ 40-50& 20\\ 50-60& 9\\ 60-70& 8\\ 70-80& 16\\ 80-90& 14\\ 90-100& 6\end{array}$

Using the table determine the Upper Quartile by drawing an ogive curve.

1. 80
2. 72
3. 76
4. 78

Q.

If the number of terms in a given data is odd, then its upper quartile is the:

1. n/4 th term

2. 3(n+1)/4 th term

3. 3n/4 th term

4. (n+1)/4 th term

Q. For the given set of numbers, the lower quartile, the upper quartile and inter quartile range is
2, 4, 13, 14, 19, 20, 27

1. 13, 20, 7
2. 4, 20, 16
3. 2, 27, 25
4. 4, 27, 25

Q.

Use graph paper for this question. The following table shows the weights in gm of a sample of 100 potatoes taken from a large consignment:

Weight (gm)	50-60	60-70	70-80	80-90	90-100	100-110	110-120	120-130
Frequency	8	10	12	16	18	14	12	10

(i) Calculate the cumulative frequencies.

(ii) Draw the cumulative frequency curve and from it determines the median weight of the potatoes.

Q.

The table shows the Distribution of the Scores obtained by 155 shooters in a shooting competition.

$\begin{array}{cc}\text{Scores}& \text{No. of shooters}\\ 0-10& 10\\ 10-20& 12\\ 20-30& 15\\ 30-40& 8\\ 40-50& 20\\ 50-60& 24\\ 60-70& 7\\ 70-80& 11\\ 80-90& 30\\ 90-100& 18\end{array}$

Use a graph sheet to draw an ogive for the distribution.

Using the graph estimate the Interquartile range

Q.

Using the frequency distribution table given below, draw 'less than ogive'. Then from the ogive, find:

interquartile range
$\begin{array}{cc}Classinterval& Frequency\\ 10-20& 2\\ 20-30& 4\\ 30-40& 6\\ 40-50& 8\\ 50-60& 10\end{array}$

1. 21

2. 22

3. 21.5

4. 22.5

Q.

The first quartile is defined as the middle number between the smallest number and the___ of the data set.

1. mode

2. frequency

3. median

4. mean

Q.

The table shows the Distribution of the Scores obtained by 155 shooters in a shooting competition.

$\begin{array}{cc}\text{Scores}& \text{No. of shooters}\\ 0-10& 10\\ 10-20& 12\\ 20-30& 15\\ 30-40& 8\\ 40-50& 20\\ 50-60& 24\\ 60-70& 7\\ 70-80& 11\\ 80-90& 30\\ 90-100& 18\end{array}$

Use a graph sheet to draw an ogive for the distribution.

Using the graph estimate the Interquartile range

1. 55

2. 84

3. 52

4. 44

Q.

If the upper quartile and the inter-quartile range of a given set of data are 16 and 7 respectively, then the lower quartile of the same set of data is:

1. 2

2. 3

3. 7

4. 9

Q.

Quartiles are those values of the variate which divide the total set of data into

1. four parts

2. two parts

3. two equal parts

4. four equal parts