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CBSE 10th Maths - Statistics- MCQ's

58749.If $x_1, x_2, x_3,….., x_n$ are the observations of a given data. Then the mean of the observations will be:
$\dfrac{Sum \:\: of \:\: observations}{Total \:\: number \:\: of \:\: observations}$
$\dfrac{Total \:\: number \:\: of \:\: observations}{Sum \:\: of \:\: observations}$
Sum of observations + Total number of observations
None of the above
Explanation:
The mean or average of observations will be equal to the ratio of sum of observations and total number of observations.
$x_{mean}=\dfrac{x_1+x_2+x_3+…..+x_n}{n}$
58750.The mode and mean is given by 7 and 8, respectively. Then the median is:
$\dfrac{1}{13}$
$\dfrac{13}{3}$
$\dfrac{23}{3}$
33
Explanation:

Using Empirical formula,

Mode = 3Median – 2 Mean

3Median = Mode + 2Mean

Median = $\dfrac{(Mode + 2Mean)}{3}$

Median = $\dfrac{[7 + 2(8)]}{3} = \dfrac{(7 + 16)}{3} = \dfrac{23}{3}$

58751.The mean of the data: 4, 10, 5, 9, 12 is;
8
10
9
15
Explanation:
Mean = $\dfrac{(4 + 10 + 5 + 9 + 12)}{5} = \dfrac{40}{5}$ = 8
58752.The median of the data 13, 15, 16, 17, 19, 20 is:
$\dfrac{30}{2}$
$\dfrac{31}{2}$
$\dfrac{33}{2}$
$\dfrac{35}{2}$
Explanation:

For the given data, there are two middle terms, 16 and 17.

Hence, median = $\dfrac{(16 + 17)}{2} = \dfrac{33}{2}$

58753.If AM of a, a+3, a+6, a+9 and a+12 is 10, then a is equal to;
1
2
3
4
Explanation:

Mean of AM = 10

$\dfrac{(a + a + 3 + a + 6 + a + 9 + a + 12)}{5}$ = 10

5a + 30 = 50

5a = 20

a = 4

58754.The class interval of a given observation is 10 to 15, then the class mark for this interval will be:
11.5
12.5
12
14
Explanation:

Class mark = $\dfrac{(Upper \: limit + Lower \: limit)}{2}$

= $\dfrac{(15 + 10)}{2}$

= $\dfrac{25}{2}$

= 12.5

58755.Construction of a cumulative frequency table is useful in determining the
mean
median
mode
all the above three measures
Explanation:

The abscissa of the point of intersection of the less than type and of the more than type cumulative frequency curves of a grouped data gives its median.

58756.The abscissa of the point of intersection of the less than type and of the more than type cumulative frequency curves of a grouped data gives its
mean
median
mode
all the three above
Explanation:

The abscissa of the point of intersection of the less than type and of the more than

type cumulative frequency curves of a grouped data gives its median.

58757.While computing mean of grouped data, we assume that the frequencies are
centred at the class marks of the classes
evenly distributed over all the classes
centred at the upper limits of the classes
centred at the lower limits of the classes
Explanation:
While computing the mean of grouped data, we assume that the frequencies are centred at the class marks of the classes.
58758. The method used to find the mean of a given data is(are):
direct method
assumed mean method
step deviation method
all the above
Explanation:

The mean for a given data can be calculated using either of the following methods.

(i) Direct method

(ii) Assumed mean method

(iii) Step deviation method

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