Grouped Frequency Distribution

Q. Find the lower and upper class limit of third class interval of the following class intervals.

1. 60 and 69
2. 70 and 79
3. 80 and 89
4. 50 and 59

Q. For class interval 20-25 write the lower class limit and the upper class limit.

Q. The average of the upper and lower class limits is called the _____ of that class interval.

1. assumed mean
2. class mark
3. class size
4. mean

Q.

Q.

In a grouped frequency distributions, the class intervals are 1-10, 11-20, 21-30, ....The class width is

1. 5.5

2. 11

3. 9

4. 10

Q. In the class interval, 45 - 55 , the lower limit is ______

1. 45
2. 55
3. 10
4. 5

Q.

Q.

In a grouped frequency distribution, what is another name for class size?

__

Q.

In grouped frequency distribution, what is another name for class size?

__

Q. Construct a frequency table from the following data:
$\begin{array}{cc}\text{Marks}& \text{No. of students}\\ \text{less than 10}& 6\\ \text{less than 20}& 15\\ \text{less than 30}& 30\\ \text{less than 40}& 39\\ \text{less than 50}& 53\\ \text{less than 60}& 70\end{array}$

Q.

The test scores for the students in Mr. Miller’s math class are shown here.

$52,61,69,76,82,84,85,90,94$.

What is the range of the test scores?

1. $82.0$

2. $77.0$

3. $42.0$

4. $22.5$

Q. The upper limit of the class interval 105-135 is ________

1. 105
2. 135
3. 125
4. 30

Q.

Following data gives the number of children in 40 families:
1, 2, 6, 5, 1, 5, 1, 3, 2, 6, 2, 3, 4, 2, 0, 4, 4, 3, 2, 2, 0, 0, 1, 2, 2, 4, 3, 2, 0, 5, 1, 2, 4, 3, 4, 1, 6, 2, 2.
Represent it in the form of a frequency distribution, taking classes 0-2, 2-4, etc.

Q. A data has highest value $120$ and the lowest value $71.A$ frequency distribution in descending order with seven classes is to be constructed. The limits of the second class interval shall be

1. $77$ and $78$
2. $113$ and $120$
3. $78$ and $85$
4. $85$ and $113$

Q. The ages of students of 10^th class, in a school are as follows. The ages are given in years months.

14$-$6, 13$-$11, 15$-$2, 16$-$0, 13$-$9, 14$-$5, 14$-$7, 14$-$0,
15$-$0, 15$-$1, 16$-$2, 14$-$1, 13$-$11, 16$-$0, 14$-$5, 14$-$0,
14$-$8, 14$-$4, 15$-$4, 15$-$9, 15$-$1, 14$-$10, 14$-$ 13$-$8

15$-$1, 14$-$1, 16$-$0, 13$-$10, 14$-$0, 15$-$0, 13$-$6, 13$-$11,
14$-$3, 14$-$8, 14$-$7, 14$-$8, 14$-$1, 15$-$0, 15$-$1, 14$-$4,
14$-$9, 14$-$9, 14$-$10, 15$-$3, 14$-$9, 13$-$10, 13$-$2, 15$-$1,

Prepare a grouped frequency distribution table (classes; 13$-$14, 14$-$15, 15$-$16, ....)

Q. Construct a frequency table with equal class intervals from the given data on the daily wages (in ₹) of 28 labourers, taking one of the class intervals as 210 - 230 (230 not included).​
220, 268, 258, 242, 210, 268, 272, 242, 311, 290, 300, 320, 319, 304, 302, 318, 306, 292, 254, 278, 210, 240, 280, 316, 306, 215, 256, 236​
What is the range of the given data?​

Q. The students of a school collected certain amounts for the Flood Relief Fund. The amounts are in rupees.
Prepare a grouped frequency distribution table.

57, 89, 62, 115, 200, 150, 130, 140, 167, 212, 117, 69, 84, 189, 207, 178, 108, 95, 142, 182, 202, 101, 88, 123, 132, 205, 195, 66, 74, 190, 210, 183, 174, 165, 156, 217, 59, 94, 118, 181, 127, 172, 169, 207, 135.

Q. Factorize: $m(x-3y{)}^2+n(3y-x)+5x-15y$

1. $(x+3y)(x-3my-n+5)$
2. $(x-3y)(mx-3my-n+5)$
3. $(x-3y)(mx+3my-n+5)$
4. $(x+3y)(mx-3y-n+5)$

Q. The daily maximum temperature in degree celcius of a city for a certain month was recorded as follows. Choosing suitable classes, prepare a grouped frequency distribution table.
$\begin{array}{cccccccccc}30.6,& 31.5,& 32.9,& 33.2,& 31.6,& 30.3,& 34.7,& 35.0,& 32.5,& 33.5,\\ 34.2,& 36.9,& 32.1,& 31.0,& 29.2,& 29.0,& 28.1,& 28.5,& 32.9,& 29.3,\\ 30.2,& 31.4,& 30.0,& 32.0,& 32.2,& 33.0,& 32.5,& 33.9,& 34.5,& 35.5.\end{array}$

Q.

1. i)The following data gives the life span, in hours, of 50 flash light batteries.

73, 72, 58, 102, 84, 76, 82, 100, 70, 72, 81, 95, 105, 101, 63, 85, 82, 90, 54, 75, 92, 75, 84, 62, 85, 80, 52, 87, 91, 85, 80, 104, 106, 72, 57, 103, 78, 79, 91, 70, 108, 97, 88, 73, 67, 101, 96, 84, 53, 86

For the above data, prepare a grouped frequency distribution by inclusive ( non-over lapping) method taking 10 as the magnitude of class intervals

Q. If $(1-100),(101-200),(201-300),(301-400),(401-500)$ and $(501-600)$ are the class intervals of a frequency distribution, then the true class width is

1. $99$
2. $99.5$
3. $100$
4. $100.5$

Q. Prepare grouped frequency distribution table by using the data given in example 1.
(Use classes : 11 − 20, 21 − 30, 31 − 40, ....., 71 − 80)

Q. A grouped frequency table with class intervals of equal sizes using $250-270$ ($270$ not included in this interval) as one of the class interval is constructed for the following data :
$268,220,368,258,242,310,272,342,$
$310,290,300,320,319,304,402,318,$
$406,292,354,278,210,240,330,316,$
$406,215,258,236.$
The frequency of the class $310-330$ is:

1. $4$
2. $5$
3. $7$
4. $6$

Q. A distribution consists of three components with frequencies $45,40$ and $15$ having their means $2,2.5,2$ respectively. The mean of the combined distribution is

1. $2.1$
2. $2.2$
3. $2.3$
4. $2.4$

Q. Convert the given frequency distribution into a continuous grouped frequency distribution:

Class Interval	Frequency
150-153	7
154-157	7
158-161	15
162-165	10
166-169	5
170-173	6

In which intervals would 153.5 and 157.5 be included?

Q.

What will be the first class interval, if the fifth class interval is 60 - 65, the fourth class interval is 55 - 60 and a total number of classes is limited to five?

1. 45-50

2. 35-40

3. 40-45

4. 60-65

Q. The distance (in km) of 40 engineers from their residence to their place of work were found as follows:
$\begin{array}{cccccccccc}5& 3& 10& 20& 25& 11& 13& 7& 12& 31\\ 19& 10& 12& 17& 18& 11& 31& 17& 16& 2\\ 7& 9& 7& 8& 3& 5& 12& 15& 18& 3\\ 12& 14& 2& 9& 6& 15& 15& 7& 6& 12\end{array}$
Construct a grouped frequency distribution table with class size 5 for the data given above taking the first interval as 0-5 (5 not included). What main feature do you observe from this tabular representation?

Q. The above data is arranged according to frequency distribution.

1. ungrouped
2. random
3. grouped

Q.

The following data tells about the number of runs scored by 20 players in a ranji match. Arrange the given data in grouped frequency distribution.

$\begin{array}{cccccccccc}11& 15& 23& 25& 31& 33& 39& 42& 43& 49\\ 51& 56& 65& 75& 79& 89& 99& 98& 92& 91\end{array}$

Q.

What is ungrouped and what is grouped frequency distribution table?