MATHS M.C.Q

1. 26

Solution:
Difference between the maximum & minimum value of the observation is called as range.
So, 32 - 6 = 26

3. 35

Solution:
Sol. Width of each of the five continuous classes in a frequency distribution is 5.
Lower class limit of the lowest class = 10
Upper class limit of the lowest class is 10 + 5 = 15
So, the five continuous classes are
10 - 15, 15 - 20, 20 - 25, 25 - 30, 30 - 35
Hence, the upper-class limit of the height class is 35.

2. 10

Solution:
The class width is the difference between the upper- or lower-class limits of consecutive classes. In this case, class width equals to the difference between the lower limits of the first two classes.
w = 10 - 0
So, the class width is 10

2. 20–30

Solution:
The number 20 is included in 20–30.
Hence, (b) is the correct answer.

3. Lower limits

Solution:
The lower limit for every class is the smallest value in that class on the other hand the upper limit for every class is the greatest value in that class. To represent ‘the more than type’ graphically, we plot the lower limits on the x-axis and cumulative frequency on the y-axis to find the median.

4. 38

Solution:
The mean of the six numbers is 23.
So the sum of six numbers is 23 × 6 = 138
After excluding one number, the mean of the remaining numbers is 20.
So the sum of five numbers is 20 × 5 = 100
The difference between them is
138 - 100 = 38

3. Frequency.

Solution:
The number of times a particular item occurs in a given data is called its Frequency.

2. 18

Solution:
The mean of five observations is 15
So the sum of these five observations is 15 × 5 = 75
The mean of first three observations is 14
So the sum of the first three observations is 14 × 3 = 42
So the sum of the last two numbers is 75 - 42 = 33
The mean of the last three observations is 17.
So sum of last three observations is 17 × 3 = 51
So the middle number is 51 - 33 = 18.

2. 9

Solution:
In statistics, the mode in a list of numbers refers to the integers that occurs most number of times.
for the set of numbers, 9 occurs three times i.e more than any other number in the list.

3. 7

Solution:
The median is the middle score for a set of data that has been arranged in ascending or descending order of magnitude.
Since 2x + 1 is in the middle of the arranged numbers, so it is median
Hence, 2x + 1 = 7
Now since 7 occurs more number of times then other numbers so mode of the list is 7.

Since mean is equal to the sum of all the values in the data set divided by the number of values in the data set also called as average.
Hence, sum of difference of all the numbers mean value will be zero.

3. 10

Solution:
The given frequency varies from 14 to 112.
So the class intervals are:
13-22, 23-32, 33-42, 43-52, 53-62, 63-72, 73-82, 83-92, 93-102, 103-112.
Number of class interval = 10.

1. 3, 3, 4

Solution:
The median is the middle score for a set of data that has been arranged in ascending or descending order of magnitude.
Mode in a list of numbers refers to the integers that occur most number of times.
For list 3, 3, 4
Both median and mode are 3.

2. 20

Solution:
The class width is the difference between the upper- or lower-class limits of consecutive classes.
In this case, class width equals to the difference between the lower limits of the first two classes.
Let, W be the class width
W = 21 - 1 = 20
So class width is 20

1. 6

Solution:
Class size is the difference between two consecutive values of the class mark.
Here, the difference between two consecutive class mark is 6.
i.e., 34 - 28 = 6

1. Cumulative frequency.

Solution:
An o-give (oh-jive), sometimes called a cumulative frequency polygon, is a type of frequency polygon that shows cumulative frequencies. An o-give graph plots cumulative frequency on the y-axis and class boundaries along the x-axis.

2. X-axis.

Solution:
In a histogram the class intervals or the groups are taken along the horizontal axis or X−axis.

4. 9

Solution:
A cumulative frequency distribution is the sum of the class and all classes below it in a frequency distribution.
Subtract the previous cumulative frequency (c.f.) from the cumulative frequency of the current class.
So frequency of the class interval 20 - 30 is 14 - 5 = 9

2. 15

Solution:
Arranging the marks in an ascending order,
We have:
14, 14, 14, 14, 15, 15, 15, 15, 16, 17, 18, 19, 19, 20
Clearly, 15 occurs maximum number of times.
Hence, mode = 15

4. 55

Solution:
Difference between the maximum & minimum value to the observations is called as range.
Let, minimum value be 'x'
75 - x = 20
So, x = 55

1. 1

Solution:
The mode in a list of numbers refers to the integers that occur most number of times.
In the given list both 8 and 9 occur two times.
So the value of x will decide the mode
If x = 8, then the mode will be 8
If x = 9, then the mode will be 9
Hence, the difference between the two modes is 1.

1. Standard deviation

Solution:
The most common measures of central tendency are mean, median and mode.
Standard deviation is a measure of the dispersion of a set of data from its mean. It is calculated as the square root of variance.
Hence standard deviation is not a measure of central tendency.

3. Most frequent value.

Solution:
Most Frequent value is called mode.

1. 20

Solution:
A cumulative frequency distribution is the sum of the class and all classes below it in a frequency distribution.
Less than 30 has the class interval 20-30. Frequency of this class interval will be corresponding to.

Marks	Cumulative frequency	Class	Frequency
Less than 10	3	1-10	3
Less than 20	17	10-20	14
Less than 30	37	20-30	20
Less than 40	92	30-40	55