### Grouping data - class-X

 Description: grouping data Number of Questions: 15 Created by: Sanjiv Memon Tags: presentation of data organisation of data collection of data collecting and displaying data data handling and analysis data mangement maths measurements and uncertainties averages and measures of spread smart tables classification of data data handling statistics handling data collecting, organising and displaying data collection, organisation and presentation of data frequency distribution tables and graphs data handling analysis
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Tally marks are used find

1. class interval

2. range

3. frequency

4. upper limit

Correct Option: C
Explanation:

Tally marks are used for counting. They represent frequrncy

Satish got the following marks in his weekly class tests out of $50$:
$48$, $32$, $36$, $42$, $38$, $35$, $39$, $49$, $34$, $14$, $32$, $37$, $31$ What should he expect in the next weekly test out of the following?
(i) between $40 - 50$
(ii) between $30 - 40$

1. Between $40-50$

2. Between $30-40$

3. Data insufficient

4. None of these

Correct Option: B
12  24  36  48  60  72
24  48  60  72  50  30
50  45  50  75  50  34

The number of students in a quiz competition scores are in the table. How many students scored $50$ marks?

1. $4$

2. $5$

3. $8$

4. $3$

Correct Option: A
Explanation:
Scores  Frequency
12  1
24  2
30  1
34  1
36  1
45  1
48  2
50  4
60  2
72  2
75  1

So, there are $4$ students scored $50$ marks.

Consider the following frequency distribution:

Class $0-10$ $0-20$ $0-30$ $0-40$ $0-50$
Frequency $3$ $8$ $14$ $20$ $25$

What is the above frequency distribution known as?

1. Cumulative distribution in more than type

2. Cumulative distribution in less than type

3. Continuous frequency distribution

4. None of the above

Correct Option: D

Consider the following statements :
1. A continuous random variable can take all values in an interval.
2. A random variable which takes a finite number of values is necessarily discrete.
3. Construction of a frequency distribution is based on data which are discrete.
Which of the above statements are correct ?

1. 1 and 2 only

2. 2 and 3 only

3. 1 and 3 only

4. 1, 2 and 3

Correct Option: A

The marks (out of 10) obtained by 28 students in a Mathematics test are listed as below :
8, 1, 2, 6, 5, 5, 5, 0, 1, 9, 7, 8, 0, 5, 8, 3, 0, 8, 10, 10, 3, 4, 8, 7, 8, 9, 2, 0
The number of students who obtained marks more than or equal to 5 is

1. 13

2. 15

3. 16

4. 17

Correct Option: D
Explanation:

Arranging the given marks in ascending order we get,

$0,0,0,0,1,1,2,2,3,3,4,5,5,5,5,6,7,7,8,8,8,8,8,8,9,9,10,10$
Students who obtained marks more than or equal $5$ are,
$5,5,5,5,6,7,7,8,8,8,8,8,8,9,9,10,10$
$\therefore$  Number of students who obtained marks more or equal to $5$ $=17$

The frequency distribution of marks obtained by $60$ students of a class is given.

X $30-34$ $40-44$ $45-49$ $50-54$ $55-59$ $60-64$
f $3$ $5$ $12$ $18$ $14$ $62$

Find mode of the distribution.

1. $42.50$

2. $52.50$

3. $52.05$

4. $42.05$

Correct Option: C
Explanation:

The given class intervals should be converted into class boundaries. Since the distribution is regular, the modal class, by inspection, is $49.5-54.5$
Further, $L _m=49.5, f _m=18, f _1=12, f _2=12, h=5$
Mode, $Z=49.5+\displaystyle\frac{18-12}{(2\times 18)-12-14}\times 5=52.5$

The median and mode of frequency distribution are 525 and 500, then mean of same frequency distribution is -

1. 75

2. 107.5

3. 527.5

4. 537.5

Correct Option: D
Explanation:

$Median = 525, Mode = 500$
$Mode = 3 median - 2 mean$
$500=3(525)-2 mean$
$2 mean=1575-500$
$mean=\frac {1075}{2}=537.5$

Mode of distribution
$Marks\begin{bmatrix} 4 & 5 & 6 & 7 & 8 \end{bmatrix}\ No\quad of\quad students\quad \begin{bmatrix} 3 & 5 & 10 & 6 & 1 \end{bmatrix}$

1. 6

2. 10

3. 8

4. 4

Correct Option: A

The cumulative frequency distribution corresponding to 20 percentile is ______.

1. 10%

2. 20%

3. 25%

4. 33%

Correct Option: B

Find a 9596 confidence interval for the population mean from the following data:

Sample size n = 65, Mean = 6300, Standard deviation = 9.5, N=1000.

1. (6298 - 6302)

2. (6301 - 6308)

3. (6290 - 4310)

4. (6288 - 6315)

Correct Option: A

What are the shortcomings of frequency distribution?

1. it does not show the details that are found in raw data

2. Once the data are grouped into classes, an individual observation has no significance in further statistical calculations

3. Statistical calculations are based only on the values of the class mark and not on the values of the observations in that class

4. All of these

Correct Option: D

If $y \, = \, x^3 \, + \, 40$, find $\displaystyle \frac{d^2y}{dx^2} =$____.

1. $(6x^2 \, + \, 4)$

2. (6x)

3. $(6x \, + \, 2x^2)$

4. (2x + 2)

Correct Option: B

A tabular summary of a set of data showing classes of the data and the fraction of the items belonging to each class is called ______________.

1. the class width

2. a relative frequency distribution

3. a cumulative relative frequency distribution

4. on ogive

Correct Option: B

In a truly normal frequency distribution _________.

1. the mean always is the same as the standard deviation

2. the mean is never the same as the mode

3. the mode is never the same as the median

4. the mean always is the same as the median

Correct Option: D
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